People interested in serving in the United States Armed Forces are often required to take theASVAB standardized test. Assuming one branch of the military has scores on the test werenormally distributed with a mean of 57 and a standard deviation of 10. A simple randomsample of 20 is taken from a population of 500.a. What is the expected value of the sampling distribution of x?b. What is the standard deviation, rounded to four decimal places, of the samplingdistribution of x?c. What is the probability, rounded to four decimal places, that the average test score in thesample will be between 50 and 60?d. What is the probability, rounded to four decimal places, that the average test score in thesample will be greater than 55?e. What is the probability, rounded to four decimal places, that the average test score in thesample will be less than 60?f. If the armed service branch wanted to know which people were in the top 15% of theirrecruits, what would the cutoff score need to be?

Sample size n=20Note: According to bartelbyquestion answer guidelines an expert can solve only three…

Answered: People interested in serving in the…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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A variable of a population has a mean of µ = 82 and a standard deviation of o = 9. a. Identify the sampling distribution of the sample mean for samples of size 81. b. In answering part (a), what assumptions did you make about the distribution of the variable? c. Can you answer part (a) if the sample size is 25 instead of 81? Why or why not? a. What is the shape of the sampling distribution? normal uniform skewed O bimodal What is the mean of the sampling distribution? Hi = (Simplify your answer.) What is the standard deviation of the sampling distribution? (Simplify your answer.) b. In answering part (a), what assumptions did you make about the distribution of the variable? A. It was assumed that the variable was normally distributed. B. No assumptions were made because, for a relatively large sample size, the sampling distribution is normal, regardless of the distribution of the variable under consideratio
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