Questions on Algebra: Probability and statistics answered by real tutors!

Tutors Answer Your Questions about Probability-and-statistics (FREE)

Question 973847: Among a random sample of 150 employees of a particular company, the mean commute distance is 29.6 miles. This mean lies 1.2 standard deviations above the mean of the sampling distribution. If a second sample of 150 employees is selected, what is the probability that for the second sample, the mean commute distance will be less than 29.6 miles?
Click here to see answer by zaimorgan(1)

Question 1011481: please guide me how to solve testing hypothesis questions ?
what is testing hypothesis and what are the steps to solve testing hypothesis ?
i am studying a book "Introduction to statistics? , 3rd edition author : ronald e. walpole...
Click here to see answer by stanbon(75887)

Question 1011416: A data set includes 105 body temperatures of healthy adult humans for which (line over top of x)x=98.7 degrees F and s=0.64 degrees F.
Complete parts (a) and (b) below. SHOW WORK
a) What is the best point estimate of the mean body temperature of all healthy humans?
The best point estimate is______ degrees F(Type an interger or a decmial)
b)Using the sample statistics, construct a 99% confidence interval estimate of the mean body temperature of all healthy humans. Do the confidence interval limits contains 98.6 degrees F? What does the sample sugesst about the use of 98.6 degrees F as the mean body temperature?
What is the confidence interval estimate of the population mean u?
_______ Do the confidence interval limits contain 98.6 degrees F? No or Yes
What does this suggest about the use of 98.6 degrees F as the mean body Temperature?
A) This suggests that the mean body temperature could very possibly be 98.6 degrees F.
B) This suggest that the mean body temperature could be lower then 98.6 degrees F
C)This suggest that the mean body temperature could be higher then 98.6 degrees F
PLEASE HELP ME!!! I AS SO LOST AND DO NOT KNOW WHERE TO BEGIN PLEASE.
Click here to see answer by stanbon(75887)

Question 1011525: Specify the null hypothesis and alternative hypothesis i each of the following cases,
(i) An automobile manufacturer wants to confirm a suppliers claim that the maximum resistance in a wiring harness is less than 50 ohms,
(ii) An investigator wants to establish the research department's claim that a new filament will increase mean bulb life of more than 3,000 hours.
Click here to see answer by stanbon(75887)

Question 1011521: As estimate of the mean time of continuous use until an
answering machine will first require service is desired. If
it can be assumed that α = 60 days, how large a sample
is needed so that one will be able to assert with 90%
confidence that the sample mean is off by at most 10
days?
Click here to see answer by stanbon(75887)

Question 1011520: An industrial engineer intends to use the mean of a random
sample of size n = 150 to estimate the average
mechanical aptitude (as measured by a certain test) of
assembly line workers in a large industry. If on the b
basis of experience, the engineer can assume that α =
6.2 for such data, what can be assert with probability
0.99 about the maximum size of his error?
Click here to see answer by stanbon(75887)

Question 1011519: Specify the null hypothesis and alternative hypothesis
in each of the following cases,
(i) An automobile manufacturer wants to confirm a
suppliers claim that the maximum resistance in a
wiring harness is less than 50 ohms,
(ii) An investigator wants to establish the research
department's claim that a new filament will increase
mean bulb life of more than 3,000 hours.
Click here to see answer by stanbon(75887)

Question 1011518: Given a random sample of 5 pints from different
production lots, we want to test whether the fat content
of a certain kind of ice cream exceeds 14%. What can
be conclude at the 0.01 level of significance about the
null hypothesis � = 14% if the Sample has mean
X = 14.9% and the standard deviation σ = 0.42%?
Click here to see answer by stanbon(75887)

Question 1011505: the audience size in a theater performing a long running detective play was monitored over a period of one year.the sizes for Monday and Wednesday nights are summariesed in the following table
audience size :50-99,100-199,200-299,300-399,400-499,500-599
number of Mondays:12,20,12,5,3,0
number of Wednesday :2,3,20,18,5,4
compare the audience sizes on Mondays and Wednesdays

Click here to see answer by ikleyn(52754)

Question 1011517: Raw material used in the production of synthetic fiber is
stored in a place which has no humidity control.
Measurements of the relative humidity in the storage
place and the moisture content of a sample of the raw
material (both in percentages) on 12 days yielded the
following results:
Humidity x 42 35 50 43 48 62 31 36 44 39 55 48
Moisture
content y 12 8 14 9 11 16 7 9 12 10 13 11
(i) Make a scatter plot to verify that it is reasonable to
assume that the regression of y on x is linear
(ii) Fit a straight line by the method of least squares,
(iii) Estimate the moisture content when humidity is 45%.
(iv) Determine the correlation coefficient.
Click here to see answer by Boreal(15235)

Question 1011270: An experiment was designed to study the performance
of 4 different detergents for cleaning fuel injectors. The
following "cleanness" readings were obtained with
specially designed equipment for 12 tanks of gas
distributed over 3 different models of engines:
Engine 1 Engine 2 Engine 3 Total
Detergent A 45 43 51 139
Detergent B 47 46 52 145
Detergent C 48 50 55 153
Detergent D 42 37 49 128
Total 182 176 207 565
Conduct a two way analysis of variance (ANOVA) present the
result on a ANOVA table and test at 0.01 level of significance
whether there are differences in the detergents or in the
engines.
Click here to see answer by ikleyn(52754)

Question 1011272: To compare two kinds of bumper guards, 6 of each kind
were mounted on a certain kind of compact car. Then
each car was run into a concrete wall at 5 miles per
hour and the following are the costs of repairs (in
memory terms) be able to assert with 90% confidence
that the sample mean is off by at most 10 days?
Bumper guard 1 107 148 123 165 102 119
Bumper guard 2 134 115 112 151 133 129
Use the 0.01 level of significance to test the difference
between the two sample means is significant.
Click here to see answer by ikleyn(52754)

Question 1011548: Which of the following statements concerning the standard normal curve is/are true (if any)?
a) The area under the standard normal curve to the left of -3 is zero.
b) The area under the standard normal curve between any two z-scores is greater than zero.
c) The area under the standard normal curve between two z-scores will be negative if both z-scores are negative.
d) The area under the standard normal curve to the left of any z-score is less than 1.
A. a, b
B. b, d
C. a, c
D. a
Click here to see answer by ikleyn(52754)

Question 1011547: A study of the amount of time it takes a mechanic to rebuild the
transmission for a 1992 Chevrolet Cavalier shows that the mean is 8.4
hours and the standard deviation is 1.77 hours. Assume that a random
sample of 40 mechanics is selected and the mean rebuild time of the
sample is computed. Assuming the mean times are normally distributed,
what percentage of sample means are greater than 7.7 hours?
A. 0.62%
B. 34.46%
C. 65.54%
D. 99.38%
Click here to see answer by ikleyn(52754)

Question 1011546: A math teacher gives two different tests to measure students� aptitude for math. Scores on the first test are normally distributed with a mean of 24 and a standard deviation of 4.5. Scores on the second test are normally distributed with a mean of 70 and a standard deviation of 11.3. Assume that the two tests use different scales to measure the same aptitude. If a student scores 29 on the first test, what would be his equivalent score on the second test? (That is, find the score that would put him in the same percentile.)
A. 87
B. 85
C. 86
D. 83
Click here to see answer by ikleyn(52754)

Question 1011545: Which of the following statements concerning areas under the standard normal curve is/are true?
a) If a z-score is negative, the area to its right is greater than 0.5.
b) If the area to the right of a z-score is less than 0.5, the z-score is negative.
c) If a z-score is positive, the area to its left is less than 0.5.
A. a, c
B. b, c
C. a, b
D. a
Click here to see answer by ikleyn(52754)

Question 1011543: The lifetimes of projector bulbs of a particular type are normally distributed with a mean of 470 hours and a standard deviation of 15 hours. What percentage of the bulbs has lifetimes that lie within 2 standard deviations of the mean on either side?
Apply the 68-95-99.7 rule to this question.
A. 68%
B. 99.7%
C. 95%
D. 100%
Click here to see answer by ikleyn(52754)

Question 1011540: The amount of Jen�s monthly phone bill is normally distributed with a mean of $50 and a standard deviation of $10. Find the 25th percentile.
A. About $46.30
B. About $43.30
C. About $43.40
D. about $43.20
Click here to see answer by ikleyn(52754)

Question 1011542: If light bulbs have lives that are normally distributed with a mean of 2500 hours and a standard deviation of 500 hours, approximately what percentage of light bulbs has a life of more than 3000 hours?
A. About 84%
B. About 68%
C. About 32%
D. About 16%
Click here to see answer by ikleyn(52754)

Question 1011400: Given a random sample of 5 pints from different
production lots, we want to test whether the fat content
of a certain kind of ice cream exceeds 14%. What can
be conclude at the 0.01 level of significance about the
null hypothesis � = 14% if the Sample has mean
barx = 14.9% and the standard deviation σ = 0.42%?

Click here to see answer by ikleyn(52754)

Question 1011541: The mean score on the exit examination for an urban high school is 63 with a standard deviation of 9. What is the standard deviation of the distribution of sample means with a sample size of 9?
A. 2
B. 3
C. 4
D. 4.1
Click here to see answer by ikleyn(52754)

Question 1011536: The area under the standard normal curve between 1 and 2 is equal to 0.1359. Scores on a particular aptitude test are normally distributed with a mean of 100 and a standard deviation of 10. Which of the following are equal to 13.59%?
a) The percentage of scores between 120 and 130
b) The percentage of scores between 110 and 120
c) The percentage of scores between 80 and 90
d) The percentage of scores between 90 and 120
A. b
B. b, c
C. d
D. a, b
Click here to see answer by ikleyn(52754)

Question 1011539: The diameters of bolts produced by a certain machine are normally distributed with a mean of 0.25 inches and a standard deviation of 0.01 inches. What percentage of bolts will have a diameter greater than 0.24 inches?
A. 79.13%
B. 82.46%
C. 84.13%
D. 84.46%
Click here to see answer by ikleyn(52754)

Question 1011538: The lifetimes of light bulbs of a particular type are normally distributed with a mean of 270 hours and a standard deviation of 11 hours. What percentage of the bulbs has lifetimes that lie within 2 standard deviations of the mean on either side?
Apply the 68-95-99.7 rule to this questions.
A. 68%
B. 1005
C. 99.7%
D. 95%
Click here to see answer by ikleyn(52754)

Question 1011537: The diameters of pencils produced by a certain machine are normally distributed with a mean of 0.30 inches and a standard deviation of 0.01 inches. In a random sample of 460 pencils, approximately how many would you expect to have a diameter less than 0.293 inches?
A. 123
B. 118
C. 112
D. 111
Click here to see answer by ikleyn(52754)

Question 1011535: Decide which of the described variables is/are likely to have a normal or near-normal distribution.
a) The heights of corn stalks in one row of corn that is half a mile long
b) The numbers of viewers of each of the channels from 202 to 550 on Direct TV at 7:00 PM CDT on the third Thursday of November 2012 (349 data values)
A. a
B. b
C. a and b
D. neither
Click here to see answer by ikleyn(52754)

Question 1011405: An experiment was designed to study the performance
of 4 different detergents for cleaning fuel injectors. The
following "cleanness" readings were obtained with
specially designed equipment for 12 tanks of gas
distributed over 3 different models of engines:
X1 E1 E2 E3 Total
D1 45 43 51 139
D2 47 46 52 145
D3 48 50 55 153
D4 42 37 49 128
T 182 176 207 565
Conduct a two way analysis of variance (ANOVA) present the
result on a ANOVA table and test at 0.01 level of significance
whether there are differences in the detergents or in the
engines.
Click here to see answer by ikleyn(52754)

Question 1011402: To compare two kinds of bumper guards, 6 of each kind
were mounted on a certain kind of compact car. Then
each car was run into a concrete wall at 5 miles per
hour and the following are the costs of repairs (in
memory terms) be able to assert with 90% confidence
that the sample mean is off by at most 10 days?
Bumper guard 1 107 148 123 165 102 119
Bumper guard 2 134 115 112 151 133 129
Use the 0.01 level of significance to test the difference
between the two sample means is significant.
Click here to see answer by ikleyn(52754)

Question 1011403: The following are the numbers of mistakes made in 4
successive days for 4 technicians working for a
photographic laboratory:
T1 T2 T3 T4
5 13 9 8
13 8 11 11
9 11 6 7
10 13 10 10
Test at the level of significance α = 0.0.5 whether the
differences among the 4 samples means can be
attributed to chance.

Click here to see answer by ikleyn(52754)

Question 1011420: The following data represents the number of units produced by four operators during three different shifts :
Shifts Operator
A B C D
I 10 8 12 13
II 10 12 14 15
III 12 10 11 14
Perform a two-way analysis of variance and interpret the result.
Click here to see answer by ikleyn(52754)

Question 1011302:
An industrial engineer intends to use the mean of a random
sample of size n = 150 to estimate the average
mechanical aptitude (as measured by a certain test) of
assembly line workers in a large industry. If on the b
basis of experience, the engineer can assume that α =
6.2 for such data, what can be assert with probability
0.99 about the maximum size of his error?
Click here to see answer by ikleyn(52754)

Question 1011399: As estimate of the mean time of continuous use until an
answering machine will first require service is desired. If
it can be assumed that α = 60 days, how large a sample
is needed so that one will be able to assert with 90%
confidence that the sample mean is off by at most 10
days?
Click here to see answer by ikleyn(52754)

Question 1011397: Raw material used in the production of synthetic fiber is
stored in a place which has no humidity control.
Measurements of the relative humidity in the storage
place and the moisture content of a sample of the raw
material (both in percentages) on 12 days yielded the
following results:
Humidity x 42 35 50 43 48 62 31 36 44 39 55 48
Moisture
content y 12 8 14 9 11 16 7 9 12 10 13 11
(i) Make a scatter plot to verify that it is reasonable to
assume that the regression of y on x is linear
(ii) Fit a straight line by the method of least squares,
(iii) Estimate the moisture content when humidity is 45%.
(iv) Determine the correlation coefficien
Click here to see answer by ikleyn(52754)

Question 1011277: The following are the scores of 15 students obtained in
the midterm and final examinations in a course in
probability and statistics
Midterm
Exam, x 70 50 80 75 90 85 60 80 65 30 85 80 70 65 40
Final
Exam, y 85 60 75 80 90 75 50 75 75 50 75 90 65 55 60
(i) Find the equation of the least square line to fit these
data,
(ii) Estimate the final examination scores of a student
who received a score of 74 in the midterm
examination.
Click here to see answer by ikleyn(52754)

Question 1011276: ) Raw material used in the production of synthetic fiber is
stored in a place which has no humidity control.
Measurements of the relative humidity in the storage
place and the moisture content of a sample of the raw
material (both in percentages) on 12 days yielded the
following results:
Humidity x 42 35 50 43 48 62 31 36 44 39 55 48
Moisture
content y 12 8 14 9 11 16 7 9 12 10 13 11
(i) Make a scatter plot to verify that it is reasonable to
assume that the regression of y on x is linear
(ii) Fit a straight line by the method of least squares,
(iii) Estimate the moisture content when humidity is 45%.
(iv) Determine the correlation coefficient.
Click here to see answer by ikleyn(52754)

Question 1011275: As estimate of the mean time of continuous use until an
answering machine will first require service is desired. If
it can be assumed that α = 60 days, how large a sample
is needed so that one will be able to assert with 90%
confidence that the sample mean is off by at most 10
days?
Click here to see answer by ikleyn(52754)

Question 1011274: Given a random sample of 5 pints from different
production lots, we want to test whether the fat content
of a certain kind of ice cream exceeds 14%. What can
be conclude at the 0.01 level of significance about the
null hypothesis � = 14% if the Sample has mean
X = 14.9% and the standard deviation σ = 0.42%?
Click here to see answer by ikleyn(52754)

Question 1011273: Specify the null hypothesis and alternative hypothesis
in each of the following cases,
(i) An automobile manufacturer wants to confirm a
suppliers claim that the maximum resistance in a
wiring harness is less than 50 ohms,
(ii) An investigator wants to establish the research
department's claim that a new filament will increase
mean bulb life of more than 3,000 hours.
Click here to see answer by ikleyn(52754)

Question 1011271: The following are the numbers of mistakes made in 4
successive days for 4 technicians working for a
photographic laboratory:
Technician I Technician II Technician III Technician IV
5 13 9 8
13 8 11 11
9 11 6 7
10 13 10 10
Test at the level of significance α = 0.0.5 whether the
differences among the 4 samples means can be
attributed to chance.
Click here to see answer by ikleyn(52754)

Question 1011544: The systolic blood pressure of 18-year-old women is normally distributed with a mean of 120 mm Hg and a standard deviation of 12 mm Hg. What percentage of 18-year-old women have a systolic blood pressure that is within 3 standard deviations of the mean on either side?
Apply the 68-95-99.7 rule to this question.
A. 68%
B. 95%
C. 100%
D. 99.7%
Click here to see answer by stanbon(75887)

Question 1011401: Q) Specify the null hypothesis and alternative hypothesis
in each of the following cases,
(i) An automobile manufacturer wants to confirm a
suppliers claim that the maximum resistance in a
wiring harness is less than 50 ohms,
(ii) An investigator wants to establish the research
department's claim that a new filament will increase
mean bulb life of more than 3,000 hours.
Click here to see answer by stanbon(75887)

Question 1011534: The systolic blood pressures of the patients at a hospital are normally distributed with a mean of 136 mm Hg and a standard deviation of 12 mm Hg. Find the two blood pressures having these properties: the mean is midway between them and 76.98% of all blood pressures are between them.
a. 121.6, 152.4
b. 121.6, 150.4
c. 123,6, 150.4
d. 122.6, 148.4
Click here to see answer by Theo(13342)

Question 1011186: The following are the scores of 15 students obtained in
the midterm and final examinations in a course in
probability and statistics
Midterm
Exam, x 70 50 80 75 90 85 60 80 65 30 85 80 70 65 40
Final
Exam, y 85 60 75 80 90 75 50 75 75 50 75 90 65 55 60
(i) Find the equation of the least square line to fit these
data,
(ii) Estimate the final examination scores of a student
who received a score of 74 in the midterm
examination.

Click here to see answer by rothauserc(4718)

Older solutions: 1..45, 46..90, 91..135, 136..180, 181..225, 226..270, 271..315, 316..360, 361..405, 406..450, 451..495, 496..540, 541..585, 586..630, 631..675, 676..720, 721..765, 766..810, 811..855, 856..900, 901..945, 946..990, 991..1035, 1036..1080, 1081..1125, 1126..1170, 1171..1215, 1216..1260, 1261..1305, 1306..1350, 1351..1395, 1396..1440, 1441..1485, 1486..1530, 1531..1575, 1576..1620, 1621..1665, 1666..1710, 1711..1755, 1756..1800, 1801..1845, 1846..1890, 1891..1935, 1936..1980, 1981..2025, 2026..2070, 2071..2115, 2116..2160, 2161..2205, 2206..2250, 2251..2295, 2296..2340, 2341..2385, 2386..2430, 2431..2475, 2476..2520, 2521..2565, 2566..2610, 2611..2655, 2656..2700, 2701..2745, 2746..2790, 2791..2835, 2836..2880, 2881..2925, 2926..2970, 2971..3015, 3016..3060, 3061..3105, 3106..3150, 3151..3195, 3196..3240, 3241..3285, 3286..3330, 3331..3375, 3376..3420, 3421..3465, 3466..3510, 3511..3555, 3556..3600, 3601..3645, 3646..3690, 3691..3735, 3736..3780, 3781..3825, 3826..3870, 3871..3915, 3916..3960, 3961..4005, 4006..4050, 4051..4095, 4096..4140, 4141..4185, 4186..4230, 4231..4275, 4276..4320, 4321..4365, 4366..4410, 4411..4455, 4456..4500, 4501..4545, 4546..4590, 4591..4635, 4636..4680, 4681..4725, 4726..4770, 4771..4815, 4816..4860, 4861..4905, 4906..4950, 4951..4995, 4996..5040, 5041..5085, 5086..5130, 5131..5175, 5176..5220, 5221..5265, 5266..5310, 5311..5355, 5356..5400, 5401..5445, 5446..5490, 5491..5535, 5536..5580, 5581..5625, 5626..5670, 5671..5715, 5716..5760, 5761..5805, 5806..5850, 5851..5895, 5896..5940, 5941..5985, 5986..6030, 6031..6075, 6076..6120, 6121..6165, 6166..6210, 6211..6255, 6256..6300, 6301..6345, 6346..6390, 6391..6435, 6436..6480, 6481..6525, 6526..6570, 6571..6615, 6616..6660, 6661..6705, 6706..6750, 6751..6795, 6796..6840, 6841..6885, 6886..6930, 6931..6975, 6976..7020, 7021..7065, 7066..7110, 7111..7155, 7156..7200, 7201..7245, 7246..7290, 7291..7335, 7336..7380, 7381..7425, 7426..7470, 7471..7515, 7516..7560, 7561..7605, 7606..7650, 7651..7695, 7696..7740, 7741..7785, 7786..7830, 7831..7875, 7876..7920, 7921..7965, 7966..8010, 8011..8055, 8056..8100, 8101..8145, 8146..8190, 8191..8235, 8236..8280, 8281..8325, 8326..8370, 8371..8415, 8416..8460, 8461..8505, 8506..8550, 8551..8595, 8596..8640, 8641..8685, 8686..8730, 8731..8775, 8776..8820, 8821..8865, 8866..8910, 8911..8955, 8956..9000, 9001..9045, 9046..9090, 9091..9135, 9136..9180, 9181..9225, 9226..9270, 9271..9315, 9316..9360, 9361..9405, 9406..9450, 9451..9495, 9496..9540, 9541..9585, 9586..9630, 9631..9675, 9676..9720, 9721..9765, 9766..9810, 9811..9855, 9856..9900, 9901..9945, 9946..9990, 9991..10035, 10036..10080, 10081..10125, 10126..10170, 10171..10215, 10216..10260, 10261..10305, 10306..10350, 10351..10395, 10396..10440, 10441..10485, 10486..10530, 10531..10575, 10576..10620, 10621..10665, 10666..10710, 10711..10755, 10756..10800, 10801..10845, 10846..10890, 10891..10935, 10936..10980, 10981..11025, 11026..11070, 11071..11115, 11116..11160, 11161..11205, 11206..11250, 11251..11295, 11296..11340, 11341..11385, 11386..11430, 11431..11475, 11476..11520, 11521..11565, 11566..11610, 11611..11655, 11656..11700, 11701..11745, 11746..11790, 11791..11835, 11836..11880, 11881..11925, 11926..11970, 11971..12015, 12016..12060, 12061..12105, 12106..12150, 12151..12195, 12196..12240, 12241..12285, 12286..12330, 12331..12375, 12376..12420, 12421..12465, 12466..12510, 12511..12555, 12556..12600, 12601..12645, 12646..12690, 12691..12735, 12736..12780, 12781..12825, 12826..12870, 12871..12915, 12916..12960, 12961..13005, 13006..13050, 13051..13095, 13096..13140, 13141..13185, 13186..13230, 13231..13275, 13276..13320, 13321..13365, 13366..13410, 13411..13455, 13456..13500, 13501..13545, 13546..13590, 13591..13635, 13636..13680, 13681..13725, 13726..13770, 13771..13815, 13816..13860, 13861..13905, 13906..13950, 13951..13995, 13996..14040, 14041..14085, 14086..14130, 14131..14175, 14176..14220, 14221..14265, 14266..14310, 14311..14355, 14356..14400, 14401..14445, 14446..14490, 14491..14535, 14536..14580, 14581..14625, 14626..14670, 14671..14715, 14716..14760, 14761..14805, 14806..14850, 14851..14895, 14896..14940, 14941..14985, 14986..15030, 15031..15075, 15076..15120, 15121..15165, 15166..15210, 15211..15255, 15256..15300, 15301..15345, 15346..15390, 15391..15435, 15436..15480, 15481..15525, 15526..15570, 15571..15615, 15616..15660, 15661..15705, 15706..15750, 15751..15795, 15796..15840, 15841..15885, 15886..15930, 15931..15975, 15976..16020, 16021..16065, 16066..16110, 16111..16155, 16156..16200, 16201..16245, 16246..16290, 16291..16335, 16336..16380, 16381..16425, 16426..16470, 16471..16515, 16516..16560, 16561..16605, 16606..16650, 16651..16695, 16696..16740, 16741..16785, 16786..16830, 16831..16875, 16876..16920, 16921..16965, 16966..17010, 17011..17055, 17056..17100, 17101..17145, 17146..17190, 17191..17235, 17236..17280, 17281..17325, 17326..17370, 17371..17415, 17416..17460, 17461..17505, 17506..17550, 17551..17595, 17596..17640, 17641..17685, 17686..17730, 17731..17775, 17776..17820, 17821..17865, 17866..17910, 17911..17955, 17956..18000, 18001..18045, 18046..18090, 18091..18135, 18136..18180, 18181..18225, 18226..18270, 18271..18315, 18316..18360, 18361..18405, 18406..18450, 18451..18495, 18496..18540, 18541..18585, 18586..18630, 18631..18675, 18676..18720, 18721..18765, 18766..18810, 18811..18855, 18856..18900, 18901..18945, 18946..18990, 18991..19035, 19036..19080, 19081..19125, 19126..19170, 19171..19215, 19216..19260, 19261..19305, 19306..19350, 19351..19395, 19396..19440, 19441..19485, 19486..19530, 19531..19575, 19576..19620, 19621..19665, 19666..19710, 19711..19755, 19756..19800, 19801..19845, 19846..19890, 19891..19935, 19936..19980, 19981..20025, 20026..20070, 20071..20115, 20116..20160, 20161..20205, 20206..20250, 20251..20295, 20296..20340, 20341..20385, 20386..20430, 20431..20475, 20476..20520, 20521..20565, 20566..20610, 20611..20655, 20656..20700, 20701..20745, 20746..20790, 20791..20835, 20836..20880, 20881..20925, 20926..20970, 20971..21015, 21016..21060, 21061..21105, 21106..21150, 21151..21195, 21196..21240, 21241..21285, 21286..21330, 21331..21375, 21376..21420, 21421..21465, 21466..21510, 21511..21555, 21556..21600, 21601..21645, 21646..21690, 21691..21735, 21736..21780, 21781..21825, 21826..21870, 21871..21915, 21916..21960, 21961..22005, 22006..22050, 22051..22095, 22096..22140, 22141..22185, 22186..22230, 22231..22275, 22276..22320, 22321..22365, 22366..22410, 22411..22455, 22456..22500, 22501..22545, 22546..22590, 22591..22635, 22636..22680, 22681..22725, 22726..22770, 22771..22815, 22816..22860, 22861..22905, 22906..22950, 22951..22995, 22996..23040, 23041..23085, 23086..23130, 23131..23175, 23176..23220, 23221..23265, 23266..23310, 23311..23355, 23356..23400, 23401..23445, 23446..23490, 23491..23535, 23536..23580, 23581..23625, 23626..23670, 23671..23715, 23716..23760, 23761..23805, 23806..23850, 23851..23895, 23896..23940, 23941..23985, 23986..24030, 24031..24075, 24076..24120, 24121..24165, 24166..24210, 24211..24255, 24256..24300, 24301..24345, 24346..24390, 24391..24435, 24436..24480, 24481..24525, 24526..24570, 24571..24615, 24616..24660, 24661..24705, 24706..24750, 24751..24795, 24796..24840, 24841..24885, 24886..24930, 24931..24975, 24976..25020, 25021..25065, 25066..25110, 25111..25155, 25156..25200, 25201..25245, 25246..25290, 25291..25335, 25336..25380, 25381..25425, 25426..25470, 25471..25515, 25516..25560, 25561..25605, 25606..25650, 25651..25695, 25696..25740, 25741..25785, 25786..25830, 25831..25875, 25876..25920, 25921..25965, 25966..26010, 26011..26055, 26056..26100, 26101..26145, 26146..26190, 26191..26235, 26236..26280, 26281..26325, 26326..26370, 26371..26415, 26416..26460, 26461..26505, 26506..26550, 26551..26595, 26596..26640, 26641..26685, 26686..26730, 26731..26775, 26776..26820, 26821..26865, 26866..26910, 26911..26955, 26956..27000, 27001..27045, 27046..27090, 27091..27135, 27136..27180, 27181..27225, 27226..27270, 27271..27315, 27316..27360, 27361..27405, 27406..27450, 27451..27495, 27496..27540, 27541..27585, 27586..27630, 27631..27675, 27676..27720, 27721..27765, 27766..27810, 27811..27855, 27856..27900, 27901..27945, 27946..27990, 27991..28035, 28036..28080, 28081..28125, 28126..28170, 28171..28215, 28216..28260, 28261..28305, 28306..28350, 28351..28395, 28396..28440, 28441..28485, 28486..28530, 28531..28575, 28576..28620, 28621..28665, 28666..28710, 28711..28755, 28756..28800, 28801..28845, 28846..28890, 28891..28935, 28936..28980, 28981..29025, 29026..29070, 29071..29115, 29116..29160, 29161..29205, 29206..29250, 29251..29295, 29296..29340, 29341..29385, 29386..29430, 29431..29475, 29476..29520, 29521..29565, 29566..29610, 29611..29655, 29656..29700, 29701..29745, 29746..29790, 29791..29835, 29836..29880, 29881..29925, 29926..29970, 29971..30015, 30016..30060, 30061..30105, 30106..30150, 30151..30195, 30196..30240, 30241..30285, 30286..30330, 30331..30375, 30376..30420, 30421..30465, 30466..30510, 30511..30555, 30556..30600, 30601..30645, 30646..30690, 30691..30735, 30736..30780, 30781..30825, 30826..30870, 30871..30915, 30916..30960, 30961..31005, 31006..31050, 31051..31095, 31096..31140, 31141..31185, 31186..31230, 31231..31275, 31276..31320, 31321..31365, 31366..31410, 31411..31455, 31456..31500, 31501..31545, 31546..31590, 31591..31635, 31636..31680, 31681..31725, 31726..31770, 31771..31815, 31816..31860, 31861..31905, 31906..31950, 31951..31995, 31996..32040, 32041..32085, 32086..32130, 32131..32175, 32176..32220, 32221..32265, 32266..32310, 32311..32355, 32356..32400, 32401..32445, 32446..32490, 32491..32535, 32536..32580, 32581..32625, 32626..32670, 32671..32715, 32716..32760, 32761..32805, 32806..32850, 32851..32895, 32896..32940, 32941..32985, 32986..33030, 33031..33075, 33076..33120, 33121..33165, 33166..33210, 33211..33255, 33256..33300, 33301..33345, 33346..33390, 33391..33435, 33436..33480, 33481..33525, 33526..33570, 33571..33615, 33616..33660, 33661..33705, 33706..33750, 33751..33795, 33796..33840, 33841..33885, 33886..33930, 33931..33975, 33976..34020, 34021..34065, 34066..34110, 34111..34155, 34156..34200, 34201..34245, 34246..34290, 34291..34335, 34336..34380, 34381..34425, 34426..34470, 34471..34515, 34516..34560, 34561..34605, 34606..34650, 34651..34695, 34696..34740, 34741..34785, 34786..34830, 34831..34875, 34876..34920, 34921..34965, 34966..35010, 35011..35055, 35056..35100, 35101..35145, 35146..35190, 35191..35235, 35236..35280, 35281..35325, 35326..35370, 35371..35415, 35416..35460, 35461..35505, 35506..35550, 35551..35595, 35596..35640, 35641..35685, 35686..35730, 35731..35775, 35776..35820, 35821..35865, 35866..35910, 35911..35955, 35956..36000, 36001..36045, 36046..36090, 36091..36135, 36136..36180, 36181..36225, 36226..36270, 36271..36315, 36316..36360, 36361..36405, 36406..36450, 36451..36495, 36496..36540, 36541..36585, 36586..36630, 36631..36675, 36676..36720, 36721..36765, 36766..36810, 36811..36855, 36856..36900, 36901..36945, 36946..36990, 36991..37035, 37036..37080, 37081..37125, 37126..37170, 37171..37215, 37216..37260, 37261..37305, 37306..37350, 37351..37395, 37396..37440, 37441..37485, 37486..37530, 37531..37575, 37576..37620, 37621..37665, 37666..37710, 37711..37755, 37756..37800, 37801..37845, 37846..37890, 37891..37935, 37936..37980, 37981..38025, 38026..38070, 38071..38115, 38116..38160, 38161..38205, 38206..38250, 38251..38295, 38296..38340, 38341..38385, 38386..38430, 38431..38475, 38476..38520, 38521..38565, 38566..38610, 38611..38655, 38656..38700, 38701..38745, 38746..38790, 38791..38835, 38836..38880, 38881..38925, 38926..38970, 38971..39015, 39016..39060, 39061..39105, 39106..39150, 39151..39195, 39196..39240, 39241..39285, 39286..39330, 39331..39375, 39376..39420, 39421..39465, 39466..39510, 39511..39555, 39556..39600, 39601..39645, 39646..39690, 39691..39735, 39736..39780, 39781..39825, 39826..39870, 39871..39915, 39916..39960, 39961..40005, 40006..40050, 40051..40095, 40096..40140, 40141..40185, 40186..40230, 40231..40275, 40276..40320, 40321..40365, 40366..40410, 40411..40455, 40456..40500, 40501..40545, 40546..40590, 40591..40635, 40636..40680, 40681..40725, 40726..40770, 40771..40815, 40816..40860, 40861..40905, 40906..40950, 40951..40995, 40996..41040, 41041..41085, 41086..41130, 41131..41175, 41176..41220, 41221..41265, 41266..41310, 41311..41355, 41356..41400, 41401..41445, 41446..41490, 41491..41535, 41536..41580, 41581..41625, 41626..41670, 41671..41715, 41716..41760, 41761..41805, 41806..41850, 41851..41895, 41896..41940, 41941..41985, 41986..42030, 42031..42075, 42076..42120, 42121..42165, 42166..42210, 42211..42255, 42256..42300, 42301..42345, 42346..42390, 42391..42435, 42436..42480, 42481..42525, 42526..42570, 42571..42615, 42616..42660, 42661..42705, 42706..42750, 42751..42795, 42796..42840, 42841..42885, 42886..42930, 42931..42975, 42976..43020, 43021..43065, 43066..43110, 43111..43155, 43156..43200, 43201..43245, 43246..43290, 43291..43335, 43336..43380, 43381..43425, 43426..43470, 43471..43515, 43516..43560, 43561..43605, 43606..43650, 43651..43695, 43696..43740, 43741..43785, 43786..43830, 43831..43875, 43876..43920, 43921..43965, 43966..44010, 44011..44055, 44056..44100, 44101..44145, 44146..44190, 44191..44235, 44236..44280, 44281..44325, 44326..44370, 44371..44415, 44416..44460, 44461..44505, 44506..44550, 44551..44595, 44596..44640, 44641..44685, 44686..44730, 44731..44775, 44776..44820, 44821..44865, 44866..44910, 44911..44955, 44956..45000, 45001..45045, 45046..45090, 45091..45135, 45136..45180, 45181..45225, 45226..45270, 45271..45315, 45316..45360, 45361..45405, 45406..45450, 45451..45495, 45496..45540, 45541..45585, 45586..45630, 45631..45675, 45676..45720, 45721..45765, 45766..45810, 45811..45855, 45856..45900, 45901..45945, 45946..45990, 45991..46035, 46036..46080, 46081..46125, 46126..46170, 46171..46215, 46216..46260, 46261..46305, 46306..46350, 46351..46395, 46396..46440, 46441..46485, 46486..46530, 46531..46575, 46576..46620, 46621..46665, 46666..46710, 46711..46755, 46756..46800, 46801..46845, 46846..46890, 46891..46935, 46936..46980, 46981..47025, 47026..47070, 47071..47115, 47116..47160, 47161..47205, 47206..47250, 47251..47295, 47296..47340, 47341..47385, 47386..47430, 47431..47475, 47476..47520, 47521..47565, 47566..47610, 47611..47655, 47656..47700, 47701..47745, 47746..47790, 47791..47835, 47836..47880, 47881..47925, 47926..47970, 47971..48015, 48016..48060, 48061..48105, 48106..48150, 48151..48195, 48196..48240, 48241..48285, 48286..48330, 48331..48375, 48376..48420, 48421..48465, 48466..48510, 48511..48555, 48556..48600, 48601..48645, 48646..48690, 48691..48735, 48736..48780, 48781..48825, 48826..48870, 48871..48915, 48916..48960, 48961..49005, 49006..49050, 49051..49095, 49096..49140, 49141..49185, 49186..49230, 49231..49275, 49276..49320, 49321..49365, 49366..49410, 49411..49455, 49456..49500, 49501..49545, 49546..49590, 49591..49635, 49636..49680, 49681..49725, 49726..49770, 49771..49815, 49816..49860, 49861..49905, 49906..49950, 49951..49995, 49996..50040, 50041..50085, 50086..50130, 50131..50175, 50176..50220, 50221..50265, 50266..50310, 50311..50355, 50356..50400, 50401..50445, 50446..50490, 50491..50535, 50536..50580, 50581..50625, 50626..50670, 50671..50715, 50716..50760, 50761..50805, 50806..50850, 50851..50895, 50896..50940, 50941..50985, 50986..51030, 51031..51075, 51076..51120, 51121..51165, 51166..51210, 51211..51255, 51256..51300, 51301..51345