Probability Stat

Question

In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 53 inches, and standard deviation of 2.3 inches.

a.) A) What is the probability that a randomly chosen child has a height of less than 53.15 inches?

Answer= 0.052 (not right)  (Round your answer to 3 decimal places.)

B) What is the probability that a randomly chosen child has a height of more than 47 inches?

Answer= 3.609 (not right)  (Round your answer to 3 decimal places.)

I just need help on the formula so i can better understand it

Answer 1

Let height = x. x is normally distributed with mean = 53 and SD = 2.3

We want to find P(x < 53.15)

Transform to standard normal distribution using z = (x - mean)/SD = (x - 53)/2.3

So P(x < 53.15) = P(z < (53.15 - 53)/2.3) = P(z < 0.065) ~ 0.526 ~ 0.053

P (x > 47) = P(z > (47-53)/2.3) = P(z > -2.609) = 1 - P(z < -2.609) = 1 - 0.0045 = 0.9955 ~ 0.996