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

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Question 1086337: 1. A typist knows from previous experience that even though she is an experienced typist, she does make mistakes. Let X be the random variable representing the number of mistakes made by the typist on a randomly selected page from all those she has typed. The probability mass function of X is given below.
Number of mistakes x 0 1 2 3 4
Probability P(X = x) 0.3 (x) 0.15 0.08 0.02
a. The value of P(X = 1) is missing. What should it be?
b. What is the probability that a random selected page will have less than 2 mistakes?
c. What is the expected value of the random variable X?
d. What is the standard deviation of the random variable X?

Click here to see answer by Fombitz(32388) About Me 

Question 1086349: Specify whether you will use a normal distribution, t-distribution or neither for the below examples:
A study is performed looking at average time exercising. 25 people participated in the study and the sample mean was 15 minutes with a sample standard deviation of 2.5 minutes. The researchers noticed that their sample means were not normally distributed

Click here to see answer by Fombitz(32388) About Me 

Question 1086352: Suppose you play a game where you flip two coins. These are the rules: You must pay $1 to play. If the coins are both Tails then you get $2, if both are Heads you get $1, and for anything else you get nothing. Would you play this game? Justify your decision.
HH 1/4 = 0.25 * $1
TT 1/4 = 0.25 * $2
HT OR TH = 2/4 OR 1/2 * 0
$1 TO START PLAYING
I'm not sure if this is how you set up this problem?

Click here to see answer by Fombitz(32388) About Me 

Question 1086345: You are provided a raw score of 250 from a normal distribution with a mean of 150 and a standard deviation of 35. Calculate the z-score for this example.
Click here to see answer by Fombitz(32388) About Me 

Question 1086360: If I produce 250 widgets and 15 are selected for quality control and 2 of the 15 are found to be defective what is my overall error rate? How do I perform this calculation?
Click here to see answer by Fombitz(32388) About Me 

Question 1086358: Samsung wants to know how long cell phone owners keep their phones before upgrading. A simple random sample of 23 cell phone owners results in a mean of 2.64 years and a standard deviation of 0.71 years. Assume the sample is drawn from a normally distributed population.
Find the 95% confidence interval of the population mean.

If you worked for Samsung and decided you wanted to be 99% confident that the sample mean is within 0.25 years of the population mean, how large of a sample would you need to take? Assume that σ=0.71 for this calculation.

Explain why the population parameter may NOT follow a normal distribution. Would you expect the data to show a positive or negative skew? Explain. If the data were not normally distributed, how would this affect the calculations for the confidence interval?

Click here to see answer by Boreal(15235) About Me 

Question 1086348: Specify whether you will use a normal distribution, t-distribution or neither for the below examples:
200 people were surveyed and it was determined that they watched an average of 65 minutes of TV per day and are normally distributed. The mean sample standard deviation is 21.3 minutes.

Click here to see answer by Boreal(15235) About Me 

Question 1086325: Samsung wants to know how long cell phone owners keep their phones before upgrading. A simple random sample of 23 cell phone owners results in a mean of 2.64 years and a standard deviation of 0.71 years. Assume the sample is drawn from a normally distributed population.
Find the 95% confidence interval of the population mean.


If you worked for Samsung and decided you wanted to be 99% confident that the sample mean is within 0.25 years of the population mean, how large of a sample would you need to take? Assume that σ=0.71 for this calculation.


Explain why the population parameter may NOT follow a normal distribution. Would you expect the data to show a positive or negative skew? Explain. If the data were not normally distributed, how would this affect the calculations for the confidence interval?

Click here to see answer by Boreal(15235) About Me 

Question 1086255: A report states that 40% of home owners had a vegetable garden. How large a sample is needed to estimate the true proportion of home owners who have vegetable gardens to within 3% with 99% confidence?
Click here to see answer by Boreal(15235) About Me 

Question 1086347: Specify whether you will use a normal distribution, t-distribution or neither for the below examples:
A study is performed assessing the average height of a sample of 20 5th graders. The mean height obtained in the sample was 56” and was approximately normally distributed. The sample standard deviation was 3.5”.

Click here to see answer by stanbon(75887) About Me 

Question 1086316: A seat is selected at random for the Fan Camera, which shows crowd reactions during the event.
What is the probability that the Fan Camera will show someone the age of 12 or older, but less than 21, during the Volley Ball game?
Give your answer as a decimal.

Click here to see answer by ikleyn(52750) About Me 

Question 1086332: A random sample of 156 fields of durum wheat has a mean yield of 26.8 bushels per acre and a standard deviation of 8.0 bushels per acre. Create a confidence interval 99%. Find a) the Margin of Error, b) the confidence interval (written as an inequality), c) the critical values and d) state whether it was a z or t distribution that you used.
Click here to see answer by stanbon(75887) About Me 

Question 1086259: In a study using 8 samples, and in which the population variance is unknown, the distribution that should be used to calculate confidence intervals is
a. a standard normal distribution.

b. a t distribution with 7 degrees of freedom.

c. a t distribution with 8 degrees of freedom.

d. a t distribution with 9 degrees of freedom.

Click here to see answer by jim_thompson5910(35256) About Me 

Question 1086254: A random sample of 70 printers discovered that 25 of them were being used in small businesses. Find the 95% limit for the population proportion of printers that are used in small businesses.

a. 0.150 < p < 0.564

b. 0.245 < p < 0.469

c. 0.263 < p < 0.452

d. 0.320 < p < 0.395

Click here to see answer by Edwin McCravy(20054) About Me 

Question 1086335: Samsung wants to know how long cell phone owners keep their phones before upgrading. A simple random sample of 23 cell phone owners results in a mean of 2.64 years and a standard deviation of 0.71 years. Assume the sample is drawn from a normally distributed population.
Find the 95% confidence interval of the population mean.


If you worked for Samsung and decided you wanted to be 99% confident that the sample mean is within 0.25 years of the population mean, how large of a sample would you need to take? Assume that σ=0.71 for this calculation.


Explain why the population parameter may NOT follow a normal distribution. Would you expect the data to show a positive or negative skew? Explain. If the data were not normally distributed, how would this affect the calculations for the confidence interval?

Click here to see answer by stanbon(75887) About Me 

Question 1086415: If X has the binomial distribution with mean 25 and probability of success 1/5, find P(X Thanks in advance.

Click here to see answer by htmentor(1343) About Me 

Question 1086421: Determine the minimum sample size needed to construct a 95% confidence interval for the mean age of employees at a company. The estimate must be accurate to within 0.5 years. Assume the sample standard deviation is 4.8 years. Your preliminary sample will be at least 30.
Click here to see answer by Boreal(15235) About Me 

Question 1086252: A food snack manufacturer samples 7 bags of pretzels off the assembly line and weighs their contents. If the sample mean is 14.2 oz. and the sample standard deviation is 0.60 oz., find the 95% confidence interval of the true mean.





Click here to see answer by rothauserc(4718) About Me 

Question 1086435: The percentages obtained in an examination are normally distributed with
mean 76% and standard deviation 15%. The top 15% of the students receive
an A and the bottom 10% receives a F and fail. Find
i) the minimum percentage to receive an A
ii) the minimum percentage to pass.

Click here to see answer by Boreal(15235) About Me 

Question 1086417: 200 laboratory sample orders were reviewed and it was determined that the mean turnaround time was 55.6 minutes for reporting the results to the physician. The turnaround times were normally distributed and showed a sample standard deviation of 5.2 minutes. The researcher s would like to construct a 90% confidence interval.
Calculate the Margin of Error:

Click here to see answer by Boreal(15235) About Me 

Question 1086243: Last year I ran in a 10K where the average completion time was 48.1 min with a standard deviation of 6.2 min. This year, runners completed the race in an average of 45.7 min with a 7.8 min standard deviation. The distribution of running times each year was approximately normal.
a. If I completed the race in 46.0 min last year and in 43.2 minutes this year, in which year did I run a better race as compared to the rest of the field?


b. If 6578 runners were in this year’s race, how many runners beat my time?


c. What time would have gotten me into the top 25%

Click here to see answer by Boreal(15235) About Me 

Question 1086445: The probability that a randomly selected 3-year-old male feral cat
will live to be 4 years old is 0.99612.
(a) What is the probability that two randomly selected 3-year-old male feral cats will live to be 4-years old?
(b) What is the probability that five randomly selected 3-year-old male feral cats will live to be 4-years old?

Click here to see answer by mathmate(429) About Me 

Question 1086240: 2. You are recruiting volunteers for a study on food choices at the grocery store. You need 32 participants, but you have 47 who apply to participate in the study.
a. How many different groups of 32 participants can you select from those who applied?
b. If three of the applicants are vegans, what is the probability of randomly selecting at least one vegan for the study?

Click here to see answer by mathmate(429) About Me 

Question 1086245: Samsung wants to know how long cell phone owners keep their phones before upgrading. A simple random sample of 23 cell phone owners results in a mean of 2.64 years and a standard deviation of 0.71 years. Assume the sample is drawn from a normally distributed population.
Find the 95% confidence interval of the population mean.


If you worked for Samsung and decided you wanted to be 99% confident that the sample mean is within 0.25 years of the population mean, how large of a sample would you need to take? Assume that σ=0.71 for this calculation.



Explain why the population parameter may NOT follow a normal distribution. Would you expect the data to show a positive or negative skew? Explain. If the data were not normally distributed, how would this affect the calculations for the confidence interval?

Click here to see answer by Alan3354(69443) About Me 

Question 1086324: 2. You are recruiting volunteers for a study on food choices at the grocery store. You need 32 participants, but you have 47 who apply to participate in the study.
a. How many different groups of 32 participants can you select from those who applied?
b. If three of the applicants are vegans, what is the probability of randomly selecting at least one vegan for the study?

Click here to see answer by stanbon(75887) About Me 

Question 1086418: 200 laboratory sample orders were reviewed and it was determined that the mean turnaround time was 55.6 minutes for reporting the results to the physician. The turnaround times were normally distributed and showed a sample standard deviation of 5.2 minutes. The researcher s would like to construct a 90% confidence interval.
Calculate the 90% confidence interval:
Present in this format:
____<<____

Click here to see answer by stanbon(75887) About Me 

Question 1086392: The standard deviation of a sample proportion p̂ gets smaller as the sample size n increases. If the population proportion is
p = 0.51,
how large a sample is needed to reduce the standard deviation of p̂ to σp hat = 0.005? (The 68−95−99.7 rule then says that about 95% of all samples will have p̂ within 0.01 of the true p. Round your answer to up to the next whole number.)

Click here to see answer by stanbon(75887) About Me 

Question 1086294: Based on the Nielsen ratings, the local CBS affiliate claims its 11 p.m. newscast reaches 31% of the viewing audience in the area. In a survey of 100 viewers, 36% indicated that they watch the late evening news on this local CBS station. What is the z test statistic?

Click here to see answer by stanbon(75887) About Me 

Question 1086258: In a sample of 40 mice, a biologist found that 42% were able to run a maze in 30 seconds or less. Find the 90% limit for the population proportion of mice who can run a maze in 30 seconds or less.
Click here to see answer by stanbon(75887) About Me 

Question 1086483: A study of nickels showed that the standard deviation of the weight of nickels is 150 milligrams. A coin counter manufacturer wishes to find the 80% confidence interval for the average weight of a nickel. How many nickels does he need to weigh to obtain an average accurate to within 10 milligrams?

a. 225

b. 369

c. 613

d. 159

Click here to see answer by jim_thompson5910(35256) About Me 

Question 1086484: Find the 95% confidence interval for the standard deviation of the lengths of pipes if a sample of 11 pipes has a standard deviation of 14.6 inches.
Click here to see answer by rothauserc(4718) About Me 
Question 1086484: Find the 95% confidence interval for the standard deviation of the lengths of pipes if a sample of 11 pipes has a standard deviation of 14.6 inches.
Click here to see answer by jim_thompson5910(35256) About Me 

Question 1085476: Question number 1
An experimental station recorded the following data:
32 29 34 31 35 35 27 32 38 37 31 38
36 35 31 36 39 41 38 31 33 41 28 30
39 39 31 37 36 32 30 39 35 32 33 38
34 42 33 33 41 30 31 34 30 33 29 32
49 30 34 33 35 33 33 35 29 35 35 42
32 35 28 36 31 32 39 26 33 34 36 32

i. Make a frequency table using five classes
ii. Draw a histogram from the table in (i) above
iii. Calculate the median, the mean and the Standard Deviation of the data set.
Question number 2
65% of men consider themselves football fans. You randomly select 8 men and ask each if he is a football fan. Find the probability that the number who consider themselves football fans is;
i. at least five
ii. Less than five
Question number 3
A newspaper is known to have a mean number of 4 typing errors per page. Find the probability that;
i. at most three typographical errors will be found on a page
ii. more than three typographical errors will be found on a page

Question number 4
A cereal maker places a game piece in its cereal boxes with a probability of winning a prize in the game equal to 1/10. Find the probability that you win your first prize with your fith purchase.
Question number 5
A civil service efficiency expert developed a test measuring job satisfaction of civil service clerks. The following information was obtained from a random sample of 10 clerks.
X 48 92 32 56 40 72 16 56 76 80
Y 13 2 14 10 14 6 17 8 3 7
Where; x is the job satisfaction index and y is the # of days absent from work in 1 year.
i. Draw a scatter diagram for the data
ii. From the scatter diagram, would you say slope is closest to 1, 0, or -1?
iii. Find the equation of the line.
Question number 6
Assume that x has a normal distribution, with the specified mean and standard deviation. Find the indicated probabilities;
i. P (3.5  x  5.8),  = 4,  = 2
ii. P (x  130),  = 120,  = 15


Question number 7
A medical researcher wishes to evaluate the effectiveness of a drug in prolonging the life of a red cell in a culture medium. Seven cultures are treated with saline (an inactive control substance) and seven others are treated with the new drug. The following survival times in days are recorded;
Control Group Treated Group
109 121
112 119
118 119
116 126
121 121
100 115
113 117
Conduct the necessary test to determine if the treatment with the new drug does in fact prolong the life of a red cell. Use  = 0.05.
Question number 8
A standardized mathematics test was given to fourth grade children in five schools in each of three different central Kenya school districts. The mean score for each school and district follows:
District 1 District 2 District 3
59 58 55
68 63 79
77 72 52
70 55 77
79 80 66

Use the 0.05 level of significance to test the claim that there are no differences in the mean scores from each school district.

Question number 9
Independent samples of tooth paste users were taken from four villages A, B, C and D. The respondents were asked which one of three common non-prescription painkillers X, Y, and Z they prefer to use. The resulting data are displayed in the table below.



VILLAGE PAINKILLER
X Y Z
A 32 39 12
B 41 23 16
C 16 18 12
D 18 27 25

Use the data to check if there is sufficient evidence to conclude that there is association between the location and the painkiller preferred by the respondents.

Click here to see answer by 29981227725404233(1) About Me 

Question 1086502: Write this expression in a single logarithm log 2 + log 5:
a. log 2.5
b. log 10
c. log  7

Click here to see answer by MathLover1(20849) About Me 

Question 1086506: You roll two six-sided number cubes. What is the probability that at least one of the numbers is even?
Click here to see answer by mathmate(429) About Me 

Question 1086513: The probability that a house in an urban area will be burglarized is 55​%. If 3333 houses are randomly​ selected, what is the probability that none of the houses will be​ burglarized?
Click here to see answer by ikleyn(52750) About Me 

Question 1086285: The null and alternate hypotheses are:H0: m1 # m2H1: m1 . m2 A random sample of 20 items from the first population showed a mean of 100 and a standard deviation of 15. A sample of 16 items for the second population showed a mean of 94 and a standard deviation of 8. Use the .05 significant level.
Click here to see answer by Boreal(15235) About Me 

Question 1086539: Evaluate: 12c6
Click here to see answer by jim_thompson5910(35256) About Me 

Question 1086535: I'm stuck at a probability Question and I don't know how to post it here so I have attached a picture! please help with the question in red block .
http://imgur.com/a/h5RXu

Click here to see answer by jim_thompson5910(35256) About Me 

Question 1086575: what is the probability of 49 and 70
Click here to see answer by Alan3354(69443) About Me 

Question 1086584: A company that makes cola drinks states that the mean weight of a 12 ounce is the same in both diet cola and regular cola. Five regular cans were sampled with a mean weight of 0.82 and a standard deviation of 0.04. Four cans of diet cola were sampled with a weight of 0.78 and a standard deviation of 0.01. Use 0.05 level of significance to test the claim
Click here to see answer by Edwin McCravy(20054) About Me 

Question 1086637: The letters of the word STATISTICS are arranged randomly.
What is the probability the arrangement will start and end with an S?

Click here to see answer by jim_thompson5910(35256) About Me 
Question 1086637: The letters of the word STATISTICS are arranged randomly.
What is the probability the arrangement will start and end with an S?

Click here to see answer by Edwin McCravy(20054) About Me 
Question 1086637: The letters of the word STATISTICS are arranged randomly.
What is the probability the arrangement will start and end with an S?

Click here to see answer by KMST(5328) About Me 
Question 1086637: The letters of the word STATISTICS are arranged randomly.
What is the probability the arrangement will start and end with an S?

Click here to see answer by ikleyn(52750) About Me 

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, 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