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 = 22.42 in, and a standard deviation given by sigma = 0.7 in. Complete parts a through c below. a. If a hat company produces hats so that they fit head circumferences between 22.1 in and 23.1 in. What is the probability that a randomly selected woman will be able to fit into one of these hafts? b. If the company wants to produce hats to fit all women except for those with the smallest 2.5% and the largest 2.5% head circumferences, what head circumferences should be accommodated? The minimum head circumference accommodated should b in Te maximum head circumference should be in

Explanation / Answer

Result:

a).

z value for 22.1, z =(22.1-22.42)/0.7 =-0.46

z value for 23.1, z =(23.1-22.42)/0.7 =0.97

P( 22.1<x<23.1) = P( -0.46<z<0.97)

=0.8315-0.3228

=0.5087

b).

z value for top 2.5% = -1.96

minimum value = 22.42-1.96*0.7 =21.048

=21.05 ( two decimals)

z value for top 2.5% = 1.96

Maximum value = 22.42+1.96*0.7 =23.792

=23.79 ( two decimals)

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