Discuss the below:
Q: A nationwide real estate company claims that its average time to sell a home is 57 days. Suppose it is known that the standard deviation of selling times is 12.3 days and that selling times are normally distributed.
a. Assuming the company's claim is true, if one home is selected at random, what is the probability that it will be sold in less than 63 days?
b. Assuming the company's claim is true, if a random sample of 9 homes is selected, what is the probability that the mean selling time will be less than 63 days?
c. Assuming the company's claim is true, if a random sample of 64 homes is selected, there is a 75% probability that the sample mean is greater than how many days?
d. Do you have to know that selling times are normally distributed to answer part (c)? Explain why or why not.
e. Suppose you doubt the company's claim that their average selling time is 57 days. To test their claim, you select a random sample of 64 homes and the sample mean number of days to sell those homes is 62 days. Do you have evidence to refute the company's claim? Explain why or why not.