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​

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%