Question

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

mu equals 23.41 inμ=23.41 in​.,

and a standard deviation given by

sigma equals 0.7 inσ=0.7 in.

Complete parts a through c below.

a. If a hat company produces​ women's hats so that they fit head circumferences between

22.822.8

in. and

23.823.8

​in., what is the probability that a randomly selected woman will be able to fit into one of these​ hats?The probability is

nothing.

​(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

3.753.75​%

and the largest

3.753.75​%

head​ circumferences, what head circumferences should be​ accommodated?The minimum head circumference accommodated should be

nothing

in.The maximum head circumference accommodated should be

nothing

in.

​(Round to two decimal places as​ needed.)

c. If

55

women are randomly​ selected, what is the probability that their mean head circumference is between

22.822.8

in. and

23.823.8

​in.? If this probability is​ high, does it suggest that an order of

55

hats will very likely fit each of

55

randomly selected​ women? Why or why​ not? (Assume that the hat company produces​ women's hats so that they fit head circumferences between

22.822.8

in. and

23.823.8

​in.)The probability is

nothing.

​(Round to four decimal places as​ needed.)

If this probability is​ high, does it suggest that an order of

55

hats will very likely fit each of

55

randomly selected​ women? Why or why​ not?

A.​Yes, the probability that an order of

55

hats will very likely fit each of

55

randomly selected women is

0.86880.8688.

B.​No, the hats must fit individual​ women, not the mean from

55

women. If all hats are made to fit head circumferences between

22.822.8

in. and

23.823.8

​in., the hats​ won't fit about

13.1213.12​%

of those women.

Answer 1

C = 0.7 = 23· ५] Ce) between ২3. ৪ ২২.৪ १(২২৪ < x <২৪ ৪) = P(<< २3:४ - २३.५) (2 < ২২.৪- २3.&\\ ০,৭ १(2 < 0.551) - १(2< -0.87) ১ ০.1।०० - ০, 1१२२ = ০. 5178 (৩) m u ৮ ३.15*|0 2(x < ५) = ০.০315 ২(2 ८ 4-২১ २(2<-).78) ০7 2 = -\,78 *0:7 +২34] २२,\6५ ২ cirumteene be marimum २३.५। + \78 *0.7 - २५०८९८

N 55 P 3.8) Paa.8 x < 23 ,8) - PC 22 23 o.7Ss 23,8 त P(2< ২২-१-२3,५) PL22-6.4L36 EP24.1316) vesy high dcupereneies niain s veLy hi Bobsbili'ly is Q4 uzen Mian Given ntewal win dhan es