Tutors Answer Your Questions about Probability-and-statistics (FREE)
Question 1161858: Suppose that the probability that a passenger will miss a flight is 0.0957. Airlines do not like flights with empty seats, but it is also not desirable to have overbooked flights because passengers must be "bumped" from the flight. Suppose that an airplane has a seating capacity of 59 passengers.
(a) If 61 tickets are sold, what is the probability that 60 or 61 passengers show up for the flight resulting in an overbooked flight?
(b) Suppose that 65 tickets are sold. What is the probability that a passenger will have to be "bumped"?
(c) For a plane with seating capacity of
52 passengers, how many tickets may be sold to keep the probability of a passenger being "bumped" below 5%?
Click here to see answer by CPhill(2264)   |
Question 1162016: Runner's World reported that a survey by Converse of people who regularly run for exercise resulted in the data shown here. The intent of the survey was to determine if the distances were independent of runners' preference for a gel-like product built into the heels of their jogging shoes. At the 1 percent level, does there appear to be any relationship? State the hypotheses.
Distance/week (miles): <3, 3-6, 7-10, 10-13, >13
Prefer Gel: 14, 18, 12, 17, 19
Do not prefer gel: 5, 5, 8, 12, 8
No opinion: 27, 17, 8, 5, 2
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Question 1162247: 1. A business owner has designed a pay scale for his employees that follow this distribution, f(x) = (20-x)/50, 10 <= x <= 20. The mean hourly rate at this business is $13.33. If an auditor randomly selects 20 employees from the company, how likely is she to observe an AVERAGE hourly rate above $15.
2. The variable x comes from the mgf, M(t) = 1/(1-nt)^alpha, where n = 2, alpha = 11.5. Find the probability that x is between 14.848 and 32.007.
Click here to see answer by CPhill(2264) |
Question 1162262: The following data represent the monthly phone use, in minutes, of a customer enrolled in a fraud prevention program for the past 20 months. The phone company decides to use the upper fence as the cutoff point for the number of minutes at which the customer should be contacted. What is the cutoff point?
317
355
433
468
471
391
408
437
455
345
519
467
425
534
425
530
513
348
521
389
Click here to see answer by CPhill(2264) |
Question 1162307: A mechanical engineer is analyzing tensile strength of steel ( API 5L X65). A sample of 7 specimens showed a sample mean of 530 MPa. The standard deviation is known to be LaTeX: MPaσ = 5 . A 95% upper confidence interval for the true mean tensile strength is:
Click here to see answer by CPhill(2264) |
Question 1162465: 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 C5 50 4C 48 62 C1 C6 44 C9 55 48
Moixture content y 12 8 14 9 11 16 7 9 12 10 1C 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 CPhill(2264) |
Question 1162467: 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 alpha = 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 CPhill(2264) |
Question 1162599: A box contains 5 yellow balls and 3 green balls. Draw 2 balls without
replacement. If X represents the number of yellow balls and Y represents the
number of green balls drawn. What is the covariance of X and Y?
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Question 1162634: An analyst estimates that the probability of default on a seven-year AA-rated bond is 0.47, while that on a seven-year A-rated bond is 0.53. The probability that they will both default is 0.45.
a. What is the probability that at least one of the bonds defaults? (Round your answer to 2 decimal places.)
b. What is the probability that neither the seven-year AA-rated bond nor the seven-year A-rated bond defaults? (Round your answer to 2 decimal places.)
c. Given that the seven-year AA-rated bond defaults, what is the probability that the seven-year A-rated bond also defaults? (Round your answer to 2 decimal places.)
Click here to see answer by CPhill(2264) |
Question 1162676: A random variable X is exponentially distributed with an expected value of 67.
a-1. What is the rate parameter λ? (Round your answer to 3 decimal places.)
a-2. What is the standard deviation of X?
b. Compute P(58 ≤ X ≤ 76). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)
c. Compute P(55 ≤ X ≤ 79). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)
Click here to see answer by CPhill(2264) |
Question 1162804: A multiple choice test has 25 questions, each with 5 possible choices, exactly one of which is correct.
The test is marked by giving four points to each correct choice, and subtracting one point for each
incorrect choice. No points are either given or subtracted for questions for which no choice is selected.
Mickey and Bianca each know the answer to 12 of the 25 questions, but are unsure about the rest.
Mickey leaves the other 13 unanswered, whereas Bianca answers them randomly, picking one choice
for each question with equal probabilities, independently between questions.
(a) Find the expectation and variance of the number of questions that Bianca gets correct.
(b) Find the expectation and variance of the mark that Bianca gets.
(c) Find the expectation and variance of the mark that Mickey gets.
Click here to see answer by CPhill(2264) |
Question 1162932: A random variable X is exponentially distributed with an expected value of 67.
a-1. What is the rate parameter λ? (Round your answer to 3 decimal places.)
a-2. What is the standard deviation of X?
b. Compute P(58 ≤ X ≤ 76). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)
c. Compute P(55 ≤ X ≤ 79). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)
Click here to see answer by CPhill(2264) |
Question 1163084: 1. Three supermarket chains in Quezon City each claim to have the lowest overall prices. As part of an investigative study on supermarket advertising, a particular news company selected nine available grocery items on a particular day. Then, the price of each selected item was checked at each of the three chains as shown in the table. Use = 0.05 to compare the prices.
Item Supermarket 1 Supermarket 2 Supermarket 3
1 55.00 50.10 52.57
2 56.00 54.05 59.45
3 84.50 93.85 102.20
4 109.80 102.65 114.00
5 117.90 103.15 113.00
6 198.50 212.25 203.90
7 248.10 243.20 248.10
8 229.95 202.95 229.45
9 271.20 268.25 287.90
Click here to see answer by CPhill(2264) |
Question 1163125: Help needed please....
Consider the following hypotheses:
H0: p ≥ 0.47
HA: p < 0.47
Compute the p-value based on the following sample information. (You may find it useful to reference the appropriate table: z table or t table) (Round "z" value to 2 decimal places. Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)
p-value
a. x = 46; n = 118 _______
b. x = 112; n = 311 _______
c. p¯ = 0.38; n = 53 _______
d. p¯ = 0.38; n = 430 _______
Click here to see answer by CPhill(2264) |
Question 1163233: H0: μ = 73
HA: μ ≠ 73
Find the p-value for this test based on the following sample information. (You may find it useful to reference the appropriate table: z table or t table)
1. x¯ = 70; s = 6.9; n = 35
A. p-value < 0.01
B. p-value > or equal to 0.10
C. 0.01 < or equal to p-value < 0.02
D. 0.05 < or equal to p-value < 0.10
E. 0.02 < or equal to p-value < 0.05
2. x¯ = 76; s = 6.9; n = 35
A. 0.01 < or equal to p-value < 0.02
B. p-value < 0.01
C. p-value > or equal to 0.10
D. 0.05 < or equal to p-value < 0.10
E. 0.02 < or equal to p-value < 0.05
Click here to see answer by CPhill(2264) |
Question 1163235: The screening process for detecting a rare disease is not perfect. Researchers have developed a blood test that is considered fairly reliable. It gives a positive reaction in 98.2% of the people who have that disease. However, it erroneously gives a positive reaction in 1.3% of the people who do not have the disease.
a. Calculate the probability of a Type I error and round your answer to 3 decimal places.
b. Calculate the probability of a Type II error and round your answer to 3 decimal places.
Click here to see answer by CPhill(2264) |
Question 1163238: Consider the following hypotheses:
H0: p ≥ 0.47
HA: p < 0.47
Compute the p-value based on the following sample information. (You may find it useful to reference the appropriate table: z table or t table) (Round "z" value to 2 decimal places. Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)
p value
a. x = 46; n = 118 _______
Click here to see answer by CPhill(2264) |
Question 1163253: Consider the following hypotheses:
H0: μ = 73
HA: μ ≠ 73
Find the p-value for this test based on the following sample information. (You may find it useful to reference the appropriate table: z table or t table)
a. x¯= 70; s = 6.9; n = 35
b. x¯ = 76; s = 6.9; n = 35
c. x¯ = 70; s = 6.4; n = 19
d. x¯ = 70; s = 6.4; n = 24
Click here to see answer by CPhill(2264) |
Question 1163400: For a sample of 29 New England cities, a sociologist studies the crime rate in each city (crimes per 100,000 residents) as a function of its poverty rate (in %) and its median income (in $1,000s). He finds that SSE = 4,136,781 and SST = 7,662,937.
Calculate the standard error of the estimate.
Click here to see answer by CPhill(2264) |
Question 1163537: A realtor studies the relationship between the size of a house (in square feet) and the property taxes (in $) owed by the owner. The table below shows a portion of the data for 20 homes in a suburb 60 miles outside of New York City. [You may find it useful to reference the t table.]
Property
Taxes Size
21860 2486
17463 2447
18232 1851
15691 1000
43998 5688
33674 2547
15233 2221
16760 1913
18247 2013
16777 1368
15164 1393
36087 3099
31021 2808
42137 3322
14374 1582
38935 4096
25336 4047
22947 2471
16177 3551
29226 2845
a-1. Calculate the sample correlation coefficient rxy. (Round intermediate calculations to at least 4 decimal places and final answers to 4 decimal places.)
a-2. Interpret rxy.
a. The correlation coefficient indicates a positive linear relationship.
b. The correlation coefficient indicates a negative linear relationship.
c. The correlation coefficient indicates no linear relationship.
b. Specify the competing hypotheses in order to determine whether the population correlation coefficient between the size of a house and property taxes differs from zero.
a. H0: ρxy = 0; HA: ρxy ≠ 0
b. H0: ρxy ≥ 0; HA: ρxy < 0
c. H0: ρxy ≤ 0; HA: ρxy > 0
c-1. Calculate the value of the test statistic. (Round intermediate calculations to at least 4 decimal places and final answer to 3 decimal places.)
c-2. Find the p-value.
a. p-value < 0.01
b. p-value > or equal to 0.10
c. 0.05 < or equal to p-value < 0.10
d. 0.02 < or equal to p-value < 0.05
e. 0.01 < or equal to p-value < 0.02
d. At the 1% significance level, what is the conclusion to the test?
a. Reject H0; we can state size and property taxes are correlated.
b. Reject H0; we cannot state size and property taxes are correlated.
c. Do not reject H0; we can state size and property taxes are correlated.
d. Do not reject H0; we cannot state size and property taxes are correlated.
Click here to see answer by CPhill(2264) |
Question 1163538: The accompanying table shows a portion of a data set that refers to the property taxes owed by a homeowner (in $) and the size of the home (in square feet) in an affluent suburb 30 miles outside New York City.
Taxes Size
21902 2370
17316 2352
18208 1930
15632 1137
43990 5626
33662 2575
15172 2222
16742 1923
18286 2041
16073 1267
15200 1398
36052 3085
31023 2869
42089 3343
14413 1632
38913 3902
25354 3940
22985 2550
16195 3563
29289 2898
1. Estimate the sample regression equation that enables us to predict property taxes on the basis of the size of the home. (Round your answers to 2 decimal places.)
Taxes =_____ +_____ Size.
2. Interpret the slope coefficient.
a. As Size increases by 1 square foot, the property taxes are predicted to increase by $7.03.
b. As Property Taxes increase by 1 dollar, the size of the house increases by 7.03 ft.
3. Predict the property taxes for a 1,600-square-foot home. (Round coefficient estimates to at least 4 decimal places and final answer to 2 decimal places.)
Taxes = _____
Click here to see answer by CPhill(2264) |
Question 1163566: Consider the following Bayesian graph:
B←A→C
The probabilities and conditional probabilities are given below:
A P(A) ¦ A B P(B︳A) ¦ A B P(C︳A)
f 0.2 ¦ f f 0.8 ¦ f f 0.3
t 0.8 ¦ f t 0.2 ¦ f t 0.7
¦ t f 0.1 ¦ t f 0.2
¦ t t 0.9 ¦ t t 0.8
a) Prove that B and C are conditionally independent given A
b) Prove that B and C are not unconditionally dependent.
Click here to see answer by CPhill(2264) |
Question 1163933: Please determine the number of bits to encode the part of speech of a sequence of words in English using a tag set of size 40. Assume the tag is a random variable. The following is the information that we have:
Among the 40 values of the tag, we know 90% of chances to be one of the four values: ART (article), P (preposition), N(noun), and V(verb). These four values are equally likely to be in a sequence. All other values of the tag has 10% chances which each of them is also equally likely to be in a sequence.
Click here to see answer by CPhill(2264) |
Question 1163935: A box contains 6 balls, 3 are blue and 3 are red. Balls are drawn successively without replacement. If random variable X is number of draws until last red ball is obtained. Find the probability density function of random variable X?
Click here to see answer by CPhill(2264) |
Question 1163947: What is the recursive relation or generating function for the following:
(a) 4, 12, 24, 24, 12, -12, -48, -96, -156, -228, ....
(b) 4, 12, 24, 24, 12, 4, 1, 1/5, 1/30, 1/210, 1/1680, ....
(c) 1, 5, 20, 60, 120, 120, 0, 0, 0, ....
(d) 1, 5, 20, 60, 120, 120, 60, 20, 5, 1, 1/6, 1/42, 1/336, ....
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Question 1163974: The random variables (X,Y) have joint pdf f(x,y) = 1/32 for the region 0 < x < 8, 0 < y < 4. The pdf is zero outside this region.
i. What are the marginal distributions of X and Y?
ii. Find the joint cdf of (X,Y) F(x,y).
iii. Find the probability P(X+Y < 4).
iv. Find the conditional probability density f(x|y)
v. Find the mean of X given Y i.e. E(X|Y).
Click here to see answer by CPhill(2264) |
Question 1163991: In a poll conducted prior to a certain election, 37% of respondents said they preferred candidate 𝐴, 33% said they preferred candidate 𝐵, and 30% said they preferred candidate 𝐶. At least how many people would have to be surveyed for you to be confident that candidate 𝐴 is truly in the lead, candidate 𝐵 is truly in second place, and candidate 𝐶 is truly in third place?
𝑛>____?
(Enter a number only.)
Click here to see answer by CPhill(2264) |
Question 1164034: A box contains one yellow, two red, and three green balls. Two balls are randomly chosen without replacement. Define the following events:
A: { One of the balls is yellow }
B: { At least one ball is red }
C: { Both balls are green }
D: { Both balls are of the same color}
Find the following conditional probabilities:
(a) P(A|B) =
(b) P(B^c|D) =
(c) P(D|C^c}) =
Click here to see answer by CPhill(2264) |
Question 1164260: A survey was conducted to see how many phone calls people made daily. The results are displayed in the table below:
Number of calls made
Frequency
1-4
14
5-8
12
9-12
6
13-16
2
17-20
Round all answers to the nearest whole number.
How many of the people surveyed make less than 5 calls per day?
What percentage of those surveyed make at least 13 calls per day?
%
How many people were surveyed?
Click here to see answer by CPhill(2264) |
Question 1164362: Suppose X and Y are independent random variables. X is exponentially distributed with mean 1/a) and Y is exponentially distributed with mean 1/b. For a random variable with mean µ define the rate of the random variable as 1/µ. a) Find the pdf of the random variable Z = min(X,Y). b) What is the mean of this distribution? c) What is the relationship between the rate of min(X,Y) and the rates of X and Y.
Click here to see answer by CPhill(2264) |
Question 1164478: Let be a standard normal random variable. Use the calculator provided, or this table, to determine the value of c.
p(Z ╪ c)= 0.7088
Carry your intermediate computations to at least four decimal places. Round your answer to two decimal places.
Click here to see answer by CPhill(2264) |
Question 1210598: assume that the readings at freezing on a bundle of thermometers are normally distributed with a mean of 0°c and a standard deviation of 1.00°c. a single thermometer is randomly selected and tested. find the probability of obtaining a reading less than -0.903°c
Click here to see answer by CPhill(2264) |
Question 5081: Help--how do i figure this one out? Driving me crazy !!!
Twenty bearded men gather. Ten have eight-inch beards, six have ten-inch beards, and four have twelve-inch beards. What is the expected length of a randomly selected man from this group?
Tried 10/20 x 6/20 x 4/20 =12inches, that doesn't seem right. Please help!
Click here to see answer by ikleyn(53875)  |
Question 46732: The traveling squad for a basketball team consists of two centers, five forwards, and four guards. In how many ways can the coach select a starting team of one center, two forwards, and two guards?
Click here to see answer by ikleyn(53875) |
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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, 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