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

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%