(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.)

Name: (A), (b) and (C) Suppose \( x \) has a distribution with a mean of 50
Uploaded: 2024-03-20T06:38:44.000Z
Channel: Bartleby
Description: (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 dist