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 $34 and the estimated standard deviation is about $9. You can usee Part A and B as a reference, but I do not need help with answering them.   c) Let us assume that x has a distribution that is approximately normal. What is the probability that x is between $32 and $36? (Round your answer to four decimal places.)   (d) In part (b), we used x, the average amount spent, computed for 60 customers. In part (c), we used x, the amount spent by only one customer. The answers to parts (b) and (c) are very different. Why would this happen? Select one of the options:   A. The standard deviation is smaller for the x distribution than it is for the x distribution. B. The mean is larger for the x distribution than it is for the x distribution.     C. The standard deviation is larger for the x distribution than it is for the x distribution. D. The x distribution is approximately normal while the x distribution is not normal. E. The sample size is smaller for the x distribution than it is for the x distribution.

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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 $34 and the estimated standard deviation is about $9.
You can usee Part A and B as a reference, but I do not need help with answering them.
 
c) Let us assume that x has a distribution that is approximately normal. What is the probability that x is between $32 and $36? (Round your answer to four decimal places.)
 
(d) In part (b), we used x, the average amount spent, computed for 60 customers. In part (c), we used x, the amount spent by only one customer. The answers to parts (b) and (c) are very different. Why would this happen? Select one of the options:
 
A. The standard deviation is smaller for the x distribution than it is for the x distribution.
B. The mean is larger for the x distribution than it is for the x distribution.    
C. The standard deviation is larger for the x distribution than it is for the x distribution.
D. The x distribution is approximately normal while the x distribution is not normal.
E. The sample size is smaller for the x distribution than it is for the x distribution.
 
In this example, x is a much more predictable or reliable statistic than x. Consider that almost all marketing strategies and sales pitches are designed for the average customer and not the individual customer. How does the central limit theorem tell us that the average customer is much more predictable than the individual customer? Select one of the options: 
 
A. The central limit theorem tells us that small sample sizes have small standard deviations on average. Thus, the average customer is more predictable than the individual customer.
 
B. The central limit theorem tells us that the standard deviation of the sample mean is much smaller than the population standard deviation. Thus, the average customer is more predictable than the individual customer.    
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