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16. [-/2.65 Points] DETAILS BBUNDERSTAT12 6.5.018.MI.S. MY NOTES ASK YOUR TEACHER 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 $32 and the estimated standard deviation is about $9. In USE SALT (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 x, the average amount spent by these customers due to impulse buying? What are the mean and standard deviation of the x distribution? O The sampling distribution of x is not normal, O The sampling distribution of x is approximately normal with mean r = 32 and standard error o= = $9. O The sampling distribution of x is approximately normal with mean us # 32 and standard error a = $0.23. O The sampling distribution of x is approximately normal with mean = 32 and standard error - = $1 42. Is it necessary to make any assumption about the x distribution? Explain your answer. O It is not necessary to make any assumption about the x distribution because u is large. It is necessary to assume that x has an approximately normal distribution. O It is not necessary to make any assumption about the x distribution because n is large. It is necessary to assume that x has a large distribution, (b) What is the probability that x is between $30 and $34? (Round your answer to four decimal places.) Let us assume that x has a distribution that is approximately normal. What is the probability that x is between $30 and $34? (Round your answer to four decimal places.) 7:07 PM 101'F D 40) 7/2/2021