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?

Answer: 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