Let $ x $ represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a newspaper article, the mean of the $ x $ distribution is about $24 and the estimated standard deviation is about $9.---**(a)** Consider a random sample of $ n = 40 $ customers, each of whom has 10 minutes of unplanned shopping time in a supermarket. From the central limit theorem, what can you say about the probability distribution of $ \overline{x} $, the average amount spent by these customers due to impulse buying? What are the mean and standard deviation of the $ \overline{x} $ distribution?- $ \text{The sampling distribution of } \overline{x} \text{ is approximately normal with mean } \mu_{\overline{x}} = 24 \text{ and standard error } \sigma_{\overline{x}} = \$0.23. $- $ \text{The sampling distribution of } \overline{x} \text{ is approximately normal with mean } \mu_{\overline{x}} = 24 \text{ and standard error } \sigma_{\overline{x}} = \$9. $- $ \text{The sampling distribution of } \overline{x} \text{ is approximately normal with mean } \mu_{\overline{x}} = 24 \text{ and standard error } \sigma_{\overline{x}} = \$1.42. $- $ \text{The sampling distribution of } \overline{x} \text{ is not normal.} $Is it necessary to make any assumption about the $ x $ distribution? Explain your answer.- $ \text{It is not necessary to make any assumption about the } x \text{ distribution because } \mu \text{ is large.} $- $ \text{It is necessary to assume that } x \text{ has a large distribution.} $- $ \text{It is necessary to assume that } x \text{ has an approximately normal distribution.} $- $ \text{It is not necessary to make any assumption about the } x \text{ distribution because } n \text{ is large.} $---**(b)** What is the probability that $ \overline{x} $ is between $21 and $27? (Round your answer

Name: Let $ x $ represent the dollar amount spent on supermarket impulse
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: Let $ x $ represent the dollar amount spent on supermarket impulse buying in a 10-minute (unplanned) shopping interval. Based on a newspaper article, the mean of the $ x $ distribution is about $24 and the estimated standard deviation is about $