Twelve-year-olds have heights that are normally distributed with a mean of heights of 57 inches and a standard deviation of 4.6 inches. what percent of 12-year-old boys will have heights less than 55 inches?

A) 33%

B) 37%

C) 42%

D) 49%

A

Step-by-step explanation:

To calculate this, the first thing we need to do is to calculate the z-score

Mathematically,

z-score = (x - mean) / SD

according to the question, X = 55 inches, mean = 57 inches and SD = 4.6 inches

we plug these values into the equation

z-score = (55-57) / 4.6 = - 2/4.6 = - 0.4348

The required probability we are trying to calculate is;

P (z < - 0.4348) or simply P (x<55)

To calculate this probability we use the standard score table

From the standard score table,

P (z < - 0.4348) = 0.33186

In percentage this is 33.186%

To the nearest percentage, this is 33%