Women have head circumferences that are normally distribution with a mean given

Question

Women have head circumferences that are normally distribution with a mean given by mu = 22.97 in., and a standard deviation given sigma = 0.8 in. Complete parts a thorough c below. a. If a hat company produces women's hats so that they head circumferences between 22.6 in, and 23.6 in what is the probability that a randomly selected woman will be able to into one of these hats? The probably is (Round to four decimal places as needed.) b. If the company wants to produce hats to all woman except for those with the smallest 3.75% and largest 3.75% head circumference, what head circumferences should be accommodated? The minimum head circumference accommodated should be in. The maximum head circumference accommodated should be in. (Round to two decimal places as needed) c. If 20 women are randomly selected, what is the probability that their mean head circumference is between 22.6 in. and 23.6 in? If this probability is high does it suggest that an order of 20 hats will very likely each 20 randomly selected women? why or why not? (Assume that the produces women's hats so that they head circumference between 22.6 in. an 23.6 in.)

Explanation / Answer

a)P(22.6<X<23.6)=P((22.6-22.97)/0.8<Z<(23.6-22.97)/0.8)=P(-0.4625<Z<0.7875)=0.7845-0.3219 =0.4626

b)for upper and lower 3.75 % , z=-/+ 0.8321

hence min head circumference =mean +*std deviation =22.30

and max head circumference =23.64

c)for 20 sample size std error =std deviation/(n)1/2 =0.1789

hence P(22.6<X<23.6)=P(-2.0684<Z<3.5218)=0.9998-0.0193 =0.9805

d)option C is correct

Related Questions

Navigate

• Browse (All)
• Browse W
• Subjects

---

---

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