-GE 2022 01/31.. 15. [-/2.65 Points] DETAILS BBUNDERSTAT12 6.5.014.5. MY NOTES ASK YOUR TEACHER Suppose the heights of 18-year-old men are approximately normally distributed, with mean 71 inches and standard deviation 4 inches. LA USE SALT a) What is the probability that an 18-year-old man selected at random is between 70 and 72 inches tall? (Round your answer to four decimal places.) (b) If a random sample of twenty-o selected, what is the probability that the mean height x is between 70 and 72 inches? (Round your answer to four decimal places.) c) Compare your answers to parts (a) and (b). Is the probability in part (b) much higher? Why would you expect this? The probability in part (b) is much higher because the standard deviation is smaller for the x di r for the x distribution. The probability in part (b) is much high d deviation is larger for the x distribution. The probability in part (b) is much higher b an is smaller for the x distribution. The probability in part (b) is much lower because the standard deviation is smaller for the x distribution. The probability in part (b) is much higher b the mean is larger for the x distribution. 16. [-/2.65 Points] DETAILS B 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 $48 and the estimated standard deviation is about $9. LA USE SALT (a) Consider a random sample of n = 60 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 ately normal with mean #x = 48 and standard error ox = $1.16. The sampling distribution = 48 and standard error ox = $0.15. The sampling distribution of = 48 and standard error ox = $9. Is it necessary to make any assumpti tion? Explain your answer. It is not necessary to make tion about the x distribution because n is large. It is not ne x distribution because , is large. It is necessary to as It is necessary to assume th ximately normal distribution. (b) What is the probability that x is between $46 and $507 (Round your answer to four decimal places.) (c) Let us assume that x has a distribution that is approximately normal. What is the probability that x is between $46 and $50? (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? The sample size is smaller for the x stribution than it is for the x distribution. The x distribution is app x distribution is not normal. The standard deviation is lar is for the x distribution. The mean is larger for the x distribution. The standard deviation is smaller for the x distribution than it is for the x distribution. MacBook Air 888 a 2 3 5 V 6 8 delete W E R T U O P