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 mu = 22.27 in, and a standard deviation given by sigma = 0.9 in. Complete parts a through c below. a. If a hat company produces women's hats so that they fit head circumferences between 21.5 in. and 22.5 in., what is the probability that a randomly selected woman will be able to fit into one of these hats? The probability is 4047 (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 1.5% and the largest 1.5% head circumferences, 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.)

Explanation / Answer

The minimum head circumference accommodated should be 20.31 in.
The maximum head circumference accommodated should be 24.22 in.
smallest 1.25% = 0.015 --> z = -2.17
largest 1.25% = 0.985 --> z = 2.17
min = (-2.17)(0.9) + 22.27 = 20.317
max = (2.17)(0.9) + 22.27 = 24.223

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