8 in Complete parts a Women have head circumferences that are normally distribut

Question

8 in Complete parts a Women have head circumferences that are normally distributed with a mean given by = 21.13 in through c below. and a standard deviation given by = a. If a hat company produces women's hats so that they fit head circumferences between 20.3 in. and 21.3 in., what is the probability that a randomly selected woman will be able to fit into one of these hats? The probability is 4344 (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 1.25% and the largest 1.25% head circumferences, what head circumferences should be accommodated? The minimum head circumference accommodated should be 19.34 in. The maximum head circumference accommodated should be 22.92n Round to two decimal places as needed.) c. If 14 women are randomly selected, what is the probability that their mean head circumference is between 20.3 in. and 21.3 in.? If this probability is high, does it suggest that an order of 14 hats will very likely fit each of 14 randomly selected women? Why or why not? (Assume that the hat company produces women's hats so that they fit head circumferences between 20.3 in. and 21.3 in.) The probability is Round to four decimal places as needed.)

Explanation / Answer

c)

for 14 women ; std error of mean =std deviation/(n)1/2 =0.8/(14)1/2 =0.2138

therfore probability that their mean head circumference is between 20.3 and 21.3 in=P(20.3<X<21.3)

=P((20.3-21.13)/0.2138<Z<(21.3-21.13)/0.2138)=P(-3.8820<Z<0.7951)=0.7867-0.0001 =0.7867

please provide option for last question so that I may help you out into that,

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