Question

In: Statistics and Probability

QUESTION 1 Let x be a random variable representing the monthly cost of joining a health...

QUESTION 1

  1. Let x be a random variable representing the monthly cost of joining a health club. We may assume that x has a normal distribution and that the population standard deviation is $5.20. A fitness magazine advertises that the mean monthly cost of joining a health club is $35. You work for a consumer advocacy group and are asked to test this claim. You find that a random sample of 40 health club monthly costs has a mean of $37.30. If you assume that the population mean is $35, find the P-value corresponding to the hypothesis that the average monthly cost is greater than $35 (i.e. right-tail test)

    A.

    0.037
    B.

    0.025
    C.

    0.012
    D.

    0.002

QUESTION 2

  1. Let x be a random variable that represents the annual salary of an elementary school teacher. The mean annual salary is reported to be $50,590. Assume the standard deviation is $1800.  If a random sample of 50 elementary school teachers is selected, what is the probability that the sample mean is less than $50,000?  

    A.

    0.0102
    B.

    0.0312
    C.

    0.373
    D.

    0.312

QUESTION 3

  1. A computer repair service found that a random sample of 45 repair costs had a mean cost of $659. Assume that the population standard deviation is $125. Calculate the margin of error, E, for a 95% confidence interval for the population mean µ.

    A.

    48.07
    B.

    34.92
    C.

    30.55
    D.

    36.52

QUESTION 4

  1. Let x be a random variable that represents the length of an Atlantic croaker fish. If x is normally distributed with a mean of 10 inches and a standard deviation of 2 inches, find the length of Croaker fish at the bottom of the top 15%.

    A.

    7.927 inches
    B.

    8.234 inches
    C.

    11.546 inches
    D.

    12.073 inches

QUESTION 5

  1. A computer repair service found that a random sample of 45 repair costs had a mean cost of $659. Assume that the population standard deviation is $125. Find the 95% confidence interval for the population mean repair cost µ of all computers.

    A.

    (612.5 , 705.5)
    B.

    (627.5 , 690.5)
    C.

    (622.5 , 695.5)
    D.

    (623.5 , 694.5)

QUESTION 6

  1. Let x be a random variable that represents the length of an Atlantic croaker fish. If x is normally distributed with a mean of 10 inches and a standard deviation of 2 inches, find the probability that length of the fish is between 8.4 inches and 10.2 inches.

    A.

    0.672
    B.

    0.328
    C.

    0.788
    D.

    0.212

QUESTION 7

  1. Let x be a random variable representing the monthly cost of joining a health club. We may assume that x has a normal distribution and that the population standard deviation is $5.20. A fitness magazine advertises that the mean monthly cost of joining a health club is $35. You work for a consumer advocacy group and are asked to test this claim. You find that a random sample of 40 health club monthly costs has a mean of $37.30. If you assume that the population mean is $35, find the standardized sample test statistic.

    A.

    3.157
    B.

    2.149
    C.

    2.797
    D.

    1.543

Solutions

Expert Solution

orchestra answered 2 years ago
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