Question

The mean ACT test score reported by the college's institutional Research Depart was 20.8, with a standard deviation of 4.8. If all possible random samples of size 40 are taken from this population, determine the following: ( Round all final answers to the nearest tenthousandth)

A) mean and standard error of the sampling distribution of the mean (use the correct name and symbol for each)

B) percent of sample means for a sample of 40 college students that are greater than 25

C) probability that sample means for samples of size 40 fall between 18 and 22

D) which sample mean can we expect to represent the first quartile

Answer 1

Given that:

Mean Score = 20.8

Standard Deviation = 4.8

n = 40

(A)

Hence, for sampling distribution,

(B)

(C)

(D) YOUR ANSWER IS 20.2881.

First quartile will be reflected by p-value of 0.25.

It reflects z-value of -0.6745.

Hence, it reflects X-value of 20.2881 using z-score function.

I hope this solves your doubt.

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