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 54.5 inches, and standard deviation of 3.4 inches. A) What is the probability that a randomly chosen child has a height of less than 61.4 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 56.3 inches?

Answer 1

A) To find the probability that a randomly chosen child has a height of less than 61.4 inches, you first need to convert the height to a z-score. The z-score is calculated by subtracting the mean from the value and dividing by the standard deviation.

So, for 61.4 inches:

Z = (61.4 - 54.5) / 3.4 = 2.03

Looking up 2.03 in the standard normal table, we find the corresponding probability is 0.979.

So, the probability that a randomly chosen child has a height of less than 61.4 inches is 0.979.

B) Similarly, to find the probability that a randomly chosen child has a height of more than 56.3 inches:

Z = (56.3 - 54.5) / 3.4 = 0.53

Looking up 0.53 in the standard normal table, we find the corresponding probability is 0.702. However, this is the probability of a child being less than 56.3 inches. Since we want the probability of a child being more than 56.3 inches, we subtract this value from 1 (since the total probability under the normal curve is 1).

So, the probability that a randomly chosen child has a height of more than 56.3 inches is 1 - 0.702 = 0.298.

Explanation: