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distribution with mean u

distribution with mean u

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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(A), (b) and (C)

Suppose \( x \) has a distribution with a mean of 50 and a standard deviation of 27. Random samples of size \( n = 36 \) are drawn. --- (a) Describe the \( \bar{x} \) distribution and compute the mean and standard deviation of the distribution. \( \bar{x} \) has a \(\_\_\_\_\_\) distribution with mean \( \mu_{\bar{x}} = \_\_\_\_\_\) and standard deviation \( \sigma_{\bar{x}} = \_\_\_\_\_\). --- (b) Find the \( z \) value corresponding to \( \bar{x} = 45.5 \). \( z = \_\_\_\_\_\) --- (c) Find \( P(\bar{x} < 45.5) \). (Round your answer to four decimal places.) \( P(\bar{x} < 45.5) = \_\_\_\_\_\) --- (d) Would it be unusual for a random sample of size 36 from the \( x \) distribution to have a sample mean less than 45.5? Explain. - \( \circ \) Yes, it would be unusual because more than 5% of all such samples have means less than 45.5. - \( \circ \) Yes, it would be unusual because less than 5% of all such samples have means less than 45.5. - \( \bullet \) No, it would not be unusual because more than 5% of all such samples have means less than 45.5. - \( \circ \) No, it would not be unusual because less than 5% of all such samples have means less than 45.5. (Checkmark indicates the correct answer.)
Transcribed Image Text:Suppose \( x \) has a distribution with a mean of 50 and a standard deviation of 27. Random samples of size \( n = 36 \) are drawn. --- (a) Describe the \( \bar{x} \) distribution and compute the mean and standard deviation of the distribution. \( \bar{x} \) has a \(\_\_\_\_\_\) distribution with mean \( \mu_{\bar{x}} = \_\_\_\_\_\) and standard deviation \( \sigma_{\bar{x}} = \_\_\_\_\_\). --- (b) Find the \( z \) value corresponding to \( \bar{x} = 45.5 \). \( z = \_\_\_\_\_\) --- (c) Find \( P(\bar{x} < 45.5) \). (Round your answer to four decimal places.) \( P(\bar{x} < 45.5) = \_\_\_\_\_\) --- (d) Would it be unusual for a random sample of size 36 from the \( x \) distribution to have a sample mean less than 45.5? Explain. - \( \circ \) Yes, it would be unusual because more than 5% of all such samples have means less than 45.5. - \( \circ \) Yes, it would be unusual because less than 5% of all such samples have means less than 45.5. - \( \bullet \) No, it would not be unusual because more than 5% of all such samples have means less than 45.5. - \( \circ \) No, it would not be unusual because less than 5% of all such samples have means less than 45.5. (Checkmark indicates the correct answer.)
Expert Solution
Step 1

According to the given scenario, X has a distribution with a mean of 50 and s.d. 27

So, X~N(50,2.72)

Random sample of n=36 are drawn.

The sample mean is x

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