MATH SOLVE

4 months ago

Q:
# the average woman's height is 65 inches with a standard deviation of 3.5 inches. what proportion of women are shorter than 62inches tall

Accepted Solution

A:

Answer:19.77%
Step-by-step explanation:Given
Mean= μ=65 inches
SD= σ=3.5 inches
We have to find the proportion of women whose height is less than 62 inches.
For that we have to calculate z-score for the given value first. The z-score of a value tells us that how many standard deviations the value is far from mean. The area to the left of the z-score gives the proportion of data that is less than the z-score value and the area to the right gives the proportion.
So,
z-score of 62= (x-μ )/σ
=(62-65)/3.5
= (-3)/3.5
z-score of 62= -0.8571
To find the area to the left of the z-score, the z-score table is used which is easily available on the internet.
The area to the left of the z-score is 1.97662.
To find the proportion/percentage of women whose height is less than 62, the area has to be multiplied by 100.
Percentage of women whose height is less than 62 inches=0.197662*100
=19.77%