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Let x represent the dollar amount spent on supermarket impulsebuying in a 10-minute (unplanned) shopping interval. Based on acertain article, the mean of the x distribution is about $34 andthe estimated standard deviation is about $9. (a) Consider a randomsample of n = 110 customers, each of whom has 10 minutes ofunplanned shopping time in a supermarket. From the central limittheorem, what can you say about the probability distribution of x,the average amount spent by these customers due to impulse buying?What are the mean and standard deviation of the x distribution? Thesampling distribution of x is not normal. The sampling distributionof x is approximately normal with mean ?x = 34 and standard error?x = $0.08. The sampling distribution of x is approximately normalwith mean ?x = 34 and standard error ?x = $0.86. The samplingdistribution of x is approximately normal with mean ?x = 34 andstandard error ?x = $9. Is it necessary to make any assumptionabout the x distribution? Explain your answer. It is necessary toassume that x has an approximately normal distribution. It isnecessary to assume that x has a large distribution. It is notnecessary to make any assumption about the x distribution because ?is large. It is not necessary to make any assumption about the xdistribution because n is large. (b) What is the probability that xis between $32 and $36? (Round your answer to four decimal places.)(c) Let us assume that x has a distribution that is approximatelynormal. What is the probability that x is between $32 and $36?(Round your answer to four decimal places.) (d) In part (b), weused x, the average amount spent, computed for 110 customers. Inpart (c), we used x, the amount spent by only one customer. Theanswers to parts (b) and (c) are very different. Why would thishappen? The x distribution is approximately normal while the xdistribution is not normal. The sample size is smaller for the xdistribution than it is for the x distribution. The standarddeviation is larger for the x distribution than it is for the xdistribution. The mean is larger for the x distribution than it isfor the x distribution. The standard deviation is smaller for the xdistribution than it is for the x distribution. In this example, xis a much more predictable or reliable statistic than x. Considerthat almost all marketing strategies and sales pitches are designedfor the average customer and not the individual customer. How doesthe central limit theorem tell us that the average customer is muchmore predictable than the individual customer? The central limittheorem tells us that the standard deviation of the sample mean ismuch smaller than the population standard deviation. Thus, theaverage customer is more predictable than the individual customer.The central limit theorem tells us that small sample sizes havesmall standard deviations on average. Thus, the average customer ismore predictable than the individual customer.