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 -21.13 in, and a standard deviation given by = 0.8 in. Complete parts a through c below. a. If a hat company produces women's hats so that they fit head circumferences between 20.3 in. and 21.3 in., what is the probability that a randomly selected woman will be able to fit into one of these hats? The probability is .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 accommodated should be in The maximum head circumference accommodated should be in (Round to two decimal places as needed.)

Explanation / Answer

Mean = 21.13

Sd = 0.8

B) minimum value

P(X < x) = 0.0125

Or, P(Z < (x - mean) /sd) = 0.0125

Or, (x - 21.13) / 0.8 = - 2.24

Or, x = 21.13 - 2.24 * 0.8

Or, x = 19.34

Minimum value = 19.34

Maximum value

P(X > x) = 0.0125

Or, P(X < x) = 1 - 0.0125

Or, P(Z < (x - 21.13)/0.8) = 0.9875

Or, (x - 21.13)/0.8 = 2.24

Or, x = 21.13 + 2.24 * 0.8

Or, x = 22.92

Maximum value = 22.92

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