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 26 and the estimated standard deviation is about 10 USE SALT a Consider a random sample of n 100 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 x the average amount spent by these customers due to impulse buying What are the mean and standard deviation of the x distribution The sampling distribution of x is not normal The sampling distribution of x is approximately normal with mean The sampling distribution of x is approximately normal with mean The sampling distribution of x is approximately normal with mean 26 and standard error 0 1 26 and standard error 1 26 and standard error o x 10 Is it necessary to make any assumption about the x distribution Explain your answer It is not necessary to make any assumption about the x distribution because n is large It is necessary to assume that x has an approximately normal distribution It is necessary to assume that x has a large distribution It is not necessary to make any assumption about the x distribution because is large b What is the probability that x is between 24 and 28 Round your answer to four decimal places Probabilities should be between 0 and 1 c Let us assume that x has a distribution that is approximately normal What is the probability that x is between 24 and 28 Round your answer to four decimal places 0 1587 d In part b we used x the average amount spent computed for 100 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 The standard deviation is larger for the x distribution than it is for the x distribution The mean is larger for the x distribution than it is for the x distribution The sample size is smaller for the x distribution than it is for the x distribution The x distribution is approximately normal while the x distribution is not normal The standard deviation 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 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 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