and a standard deviation given by -08 n. Com Women have head circumferences that

Question

and a standard deviation given by -08 n. Com Women have head circumferences that are normally distributed with a mean given by-23 27 in through c below e e parts a 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 0.4344 (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 accom modated should be-in. The maximum head circumference accommodated should bein (Round to two decimal places as needed.)

Explanation / Answer

a)

b) for 1.25 % on both tails; critical z =2.2414

therefore maximum hed =mean +z*std deviation=25.06 in

mInimum hed =mean +z*std deviation=21.48 in

for normal distribution z score =(X-)/ here mean=       = 23.270 std deviation   == 0.8

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