Scores at a local high school on the American College Testing (ACT) college entrance exam follow the normal distribution with a mean of 18 and a standard deviation of 8.  A guidance counselor takes a random sample of 20 students and calculates the mean score, ?¯x¯. (a) Calculate the mean and standard deviation of the sampling distribution of ?¯x¯. (b) Interpret the standard deviation from part (a). (c) Find the probability that a sample of 20 students has a mean score of 19.5 or more.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.4: Distributions Of Data
Problem 19PFA
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Scores at a local high school on the American College Testing (ACT) college entrance exam follow the normal distribution with a mean of 18 and a standard deviation of 8.  A guidance counselor takes a random sample of 20 students and calculates the mean score, ?¯x¯.
(a) Calculate the mean and standard deviation of the sampling distribution of ?¯x¯.
(b) Interpret the standard deviation from part (a).
(c) Find the probability that a sample of 20 students has a mean score of 19.5 or more.

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