9 ### Educational Content: Sampling Distribution**Problem Statement:**A simple random sample of size \( n = 64 \) is obtained from a population with a mean \( \mu = 80 \) and a standard deviation \( \sigma = 32 \).**Questions:**(a) **Describe the sampling distribution of \( \bar{x} \):**(b) **What is \( P(\bar{x} > 88) \)?**(c) **What is \( P(\bar{x} > 72) \)?**(d) **What is \( P(76.8 < \bar{x} < 86.2) \)?**---**Multiple Choice:**(a) Choose the correct description of the shape of the sampling distribution of \( \bar{x} \).- A. The distribution is uniform.- B. The distribution is skewed left.- C. The distribution is skewed right.- D. The distribution is approximately normal.- E. The shape of the distribution is unknown.**Explanation:**When a simple random sample is taken and the sample size is large enough (typically \( n > 30 \)), the Central Limit Theorem suggests that the sampling distribution of the sample mean \( \bar{x} \) will be approximately normal, regardless of the shape of the population distribution. Given the sample size of 64, which is greater than 30, the correct choice for part (a) is likely:- **D. The distribution is approximately normal.**

Name: 9 ### Educational Content: Sampling Distribution**Problem Statement:**
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: 9 ### Educational Content: Sampling Distribution**Problem Statement:**A simple random sample of size \( n = 64 \) is obtained from a population with a mean \( \mu = 80 \) and a standard deviation \( \sigma = 32 \).**Questions:**(a) **Describe the sam

According to the central limit theorem, if the sample size is sufficiently large, i.e., n =30 or >30, the sampling distribution of the mean approaches approximate to normal distribution. For this case, the distribution of the means will always be approximately normal distribution because the sample size is greater than 30. Hence, the correct option is, D. The distribution is approximately normal.