Let x represent the dollar amount spent on supermarketimpulse buying in a 10-minute (unplanned) shopping interval. Basedon a certain article, the mean of the x distribution isabout $32 and the estimated standard deviation is about $7.

(a) Consider a random sample of n = 80 customers, eachof whom has 10 minutes of unplanned shopping time in a supermarket.From the central limit theorem, what can you say about theprobability distribution of x, the average amount spent bythese customers due to impulse buying? What are the mean andstandard deviation of the x distribution?

The sampling distribution of x is approximately normalwith mean ?_x = 32 and standard error?_x = $0.09. The sampling distributionof x is not normal.     The samplingdistribution of x is approximately normal with mean?_x = 32 and standard error?_x = $7. The sampling distribution ofx is approximately normal with mean?_x = 32 and standard error?_x = $0.78.

Is it necessary to make any assumption about the xdistribution? Explain your answer.

It is necessary to assume that x has an approximatelynormal distribution. It is necessary to assume that x hasa large distribution.     It is not necessaryto make any assumption about the x distribution because? is large. It is not necessary to make any assumptionabout the x distribution because n is large.

(b) What is the probability that x is between $30 and$34? (Round your answer to four decimal places.)

(c) Let us assume that x has a distribution that is approximately normal. What is theprobability that x is between $30 and $34?(Round your answer to four decimal places.)
(d) In part (b), we used x,the average amount spent, computed for 80 customers. In part (c), we used x,the amount spent by only one customer. The answers to parts (b) and (c) are very different. Whywould this happen?

The sample size is smaller for the x distributionthan it is for the x distribution. The mean is larger for the x distributionthan it is for the x distribution.     The standard deviation is smaller for the x distributionthan it is for the x distribution. The xdistribution is approximately normal while the x distribution is not normal. The standard deviation is larger for the x distributionthan it is for the x distribution.