The heights of women in the United States are normally distributed with a mean of 63.7 inches and a standard deviation of 2.7 inches. If you randomly select a woman in the United States, what is the probability that she will be between 65 and 67 inches tall?

the probability that she will be between 65 and 67 inches tall is 0.2077

Step-by-step explanation:

Since heights of women in the United States are normally distributed, we would apply the formula for normal distribution which is expressed as

z = (x - µ)/σ

Where

x = heights of women.

µ = mean height

σ = standard deviation

From the information given,

µ = 63.7 inches

σ = 2.7 inches

We want to find the probability that the height of a woman selected will be between 65 and 67 inches. It is expressed as

P(65 ≤ x ≤ 67)

For x = 65,

z = (65 - 63.75)/2.7 = 0.46

Looking at the normal distribution table, the probability corresponding to the z score is 0.6772

For x = 67,

z = (67 - 63.75)/2.7 = 1.2

Looking at the normal distribution table, the probability corresponding to the z score is 0.8849

P(65 ≤ x ≤ 67) = 0.8849 - 0.6772

= 0.2077