In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 54.4 inches, and standard deviation of 7.9 inches.

A) What is the probability that a randomly chosen child has a height of less than 46.35 inches?

Answer=

(Round your answer to 3 decimal places.)

B) What is the probability that a randomly chosen child has a height of more than 38.6 inches?

Answer=

Given Information:  

Mean height of ten year children = μ =  54.4 inches

Standard deviation = σ = 7.9 inches

Required Information:  

A) What is the probability that a randomly chosen child has a height of less than 46.35 inches?

B) What is the probability that a randomly chosen child has a height of more than 38.6 inches?

Explanation:

Let X is the random variable that represents height measurements of ten-year-old children with mean of 54.4 inches and standard deviation of 7.9 inches.

A) The probability that a randomly chosen child has a height of less than 46.35 inches is given by

From the z-table , the z-score corresponding to -1.02 is 0.1538  

Therefore, 15.38% children has a height of less than 46.35 inches.

B) The probability that a randomly chosen child has a height of more than 38.6 inches is given by

From the z-table , the z-score corresponding to -2 is 0.0227

Therefore, 97.73% children has a height of greater than 38.6 inches.