Women have head circumferences that are normally distributed with a mean given b

Question

Women have head circumferences that are normally distributed with a mean given by ? 2429 ?n and a standard deviation given by ? 12in Complete parts a through c below. a. If a hat company produces women's hats so that they fit head circumferences between 23.5 in. and 24.5 in., what is the probability that a randomly selected woman will be able to fit into one of these hats? in. and 24.5 in., wh 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 beim The maximum head circumference accommodated should ben Round to two decimal places as needed.) in. c. If 12 women are randomly selected, what is the probability that their mean head circumference is between 23.5 in. and 24.5 in.? If this probability is high, does it suggest that an order of 12 hats will very likely fit each of 12 randomly selected women? Why or why not? (Assume that the hat company produces women's hats so that they fit head circumferences between 23.5 in. and 24.5 in.) The probability is (Round to four decimal places as needed.) If this probability is high, does it suggest that an order of 12 hats will very likely fit each of 12 randomly selected women? Why or why not? OA. No, the hats must fit individual women, not the mean from 12 women. If all hats are made to fit head circumferences between 23.5 in. and 24.5 in., the hats won't fit about 28.22% of those women. ( B. Yes, the probability that an order of 12 hats will very likely fit each of 12 randomly selected women is 0 7179 O c. Yes, the order of 12 hats will very likely fit each of 12 randomly selected women because both 23.5 in, and 24.5 in lie inside the range found in part (b) 0 D. No, the hats must fit individual women, not the mean from 12 women. If all hats are made to fit head circumferences between 23.5 in. and 24.5 in., the hats won't fit about half of those women

Explanation / Answer

a)

( please try 0.3143 if above does not work due to rounding)

b) for 2.5% end values ; critical z =1.96

minimum head cicum ference =mean +Z*std deviation =21.94

maximum head cicum ference =mean +Z*std deviation =26.64

c)

( please try 0.7165 if above does not work due to rounding)

option D is correct

for normal distribution z score =(X-?)/? here mean=       ?= 24.29 std deviation   =?= 1.2000

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.