The mean selling price of new homes in a city over a year was $115,000. The population standard deviation was $25,000. A random sample of 100 new homes sales from this city was taken.

(a) What is the probability that the sample mean selling price was more than $110,000?

(b) What is the probability that the sample mean selling price was between $113,000 and $117,000?

(c) What is the probability that the sample mean selling price was between $114,000 and $116,000?

(d) Without doing the calculations, state in which of the following ranges the sample mean selling price is most likely to lie: $113,000-$115,000, $114,000-$116,000, $115,000-$117,000, $116,000-$118,000

(e) Suppose that, after you had done the above calculations, a friend asserted that the pop- ulation distribution of selling prices of new homes in this city was almost certainly not normal. How would you respond?