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 53.8 inches, and standard deviation of 7.5 inches. A) What is the probability that a randomly chosen child has a height of less than 62.95 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 44.4 inches? Answer= (Round your answer to 3 decimal places.) Calculator Submit Question Question 10

Answer 1

A) 0.889

B) 0.895

Explanation:

Mean of 53.8 inches, and Standard deviation of 7.5 inches.

We solve using z score formula

z = (x-μ)/σ, where

x is the raw score

μ is the population mean

σ is the population standard deviation.

A) What is the probability that a randomly chosen child has a height of less than 62.95 inches?

For x < 62.95

z = 62.95 - 53.8/7.5

z = 1.22

Probabilityvalue from Z-Table:

P(x<62.95) = 0.88877

Approximately = 0.889

B) What is the probability that a randomly chosen child has a height of more than 44.4 inches?

For x > 44.4 inches

z = 44.4 - 53.8/7.5

z = -1.25333

Probability value from Z-Table:

P(x<44.4) = 0.10504

P(x>44.4) = 1 - P(x<44.4) = 0.89496

Approximately = 0.895