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 56.2 inches, and standard deviation of 3.3 inches.

A) What is the probability that a randomly chosen child has a height of less than 63.75 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 60 inches? Answer= ______________ (Round your answer to 3 decimal places.)

Answer 1

A) 0.989

B) 0.875

Explanation:

Let the X denote height measurements of ten year old children.

Thus, X follows the Normal distribution with mean = 56.2 inches and standard deviation = 3.3 inches.

A) we have to find the probability that a randomly chosen child has a height of less than 63.75 inches.

That is;

P(X < 63.75)

using z score formula, we have;

Z = (X - μ)/σ

Where, μ is mean and σ is standard deviation.

Thus;

Z = (63.75 - 56.2)/3.3

Z = 2.288

From z distribution table, we have the value as approximately 0.989

B) Similarly, using z score formula, we have;

Z = (X - μ)/σ

Where, μ is mean and σ is standard deviation.

Thus;

we have to find the probability that a randomly chosen child has a height of more than 60 inches.

Z = (60 - 56.2)/3.3

Z = 1.1515

From z-tables, the value is approximately 0.875