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