 # Mathematics And Statistics Questions

Subject Mathematics Statistics-R Programming

## Question

QUESTION 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

QUESTION 2
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 3
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 4
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
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 6
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 7
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)

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Question 1: The answer is option B.
Question 2: The answer is option D....

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