Answer :
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
The probability that she will be between 65 and 67 inches tall is 20.44%.
Z score
Z score is used to determine by how many standard deviations the raw score is above or below the mean. The z score is given by:
z = (x - μ)/σ
where x is the raw score, μ is the mean and σ is the standard deviation.
Given mean 63.7, standard deviation = 2.7. Hence:
For x = 65:
z= (65 - 63.7)/2.7 = 0.48
For x = 67:
z= (65 - 63.7)/2.7 = 1.22
P(0.48 < z < 1.22) = P(z < 1.22) - P(z < 0.48) = 0.8888 - 0.6844 = 20.44%
The probability that she will be between 65 and 67 inches tall is 20.44%.
Find out more on Z score at: https://brainly.com/question/25638875