Question

Women have head circumferences that are normally distributed with a mean given by 22.13 and a standard deviation given by 0.9. Complete parts a through c.

A. If a hat company produces women’s hats so that they fit head circumferences between 21.9 and 22.9 what is the probability that a randomly selected women will be able to fit into one of these hats?

The probability is..

B. If the company wants to produce hats to fill 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 should be?

The maximum head circumference should be?

Answer 1

Solution:-

Mean = 22.13, S.D = 0.90

A) The probability is 0.408.

x₁ = 21.9

x₂ = 22.9

By applying normal distruibution:-

z₁ = - 0.26

z₂ = 0.86

P(- 0.26 < z < 0.86) = P(z > - 0.26) - P(z > 0.86)

P(- 0.26 < z < 0.86) = 0.603 - 0.195

P(- 0.26 < z < 0.86) = 0.408

B) The minimum and maxiumum head circumference should be 20.366 and 23.894.

p-value for the smallest 2.5% and the largest 2.5% head circumferences = 0.025 and 0.975

z-score for the p-value = + 1.96

By applying normal distruibution:-

x₁ = 20.366

x₂ = 23.894