Question

Women have head circumferences that are normally distributed with a mean given by ​u= 23.76in, and a standard deviation given by o= 1.1in.

a. If a hat company produces​ women's hats so that they fit head circumferences between 23.1 in. and 24.1 ​in., what is the probability that a randomly selected woman will be able to fit into one of these​ hats?

The probability is . ___. ​(Round to four decimal places as​ needed.)

b. If the company wants to produce hats to fit all women except for those with the smallest ​2.5% and the largest ​2.5% head​circumferences, what head circumferences should be​accommodated?

The minimum head circumference accommodated should be ___in. (Round to two decimal places as​ needed.)

The maximum head circumference accommodated should be nothing ___in. ​(Round to two decimal places as​ needed.)

c. If 8 women are randomly​ selected, what is the probability that their mean head circumference is between 23.1 in. and 24.1 ​in.? If this probability is​ high, does it suggest that an order of 8 hats will very likely fit each of 8 randomly selected​ women? Why or why​ not? (Assume that the hat company produces​ women's hats so that they fit head circumferences between 23.1 in. and 24.1 ​in.)

The probability is ___. ​(Round to four decimal places as​ needed.)

Answer 1