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 1

To find the probability that a randomly chosen child has a height of less than 63.75 inches, we need to calculate the z-score and then find the corresponding probability on a standard normal distribution table. The probability is approximately 0.9883.

Step-by-step explanation:

In order to find the probability that a randomly chosen child has a height of less than 63.75 inches, we need to calculate the z-score and then find the corresponding probability on a standard normal distribution table.

To find the z-score, we use the formula:

z = (x - μ) / σ

Where x is the value we want to find the probability for, μ is the mean height, and σ is the standard deviation. Substituting the given values, we get:

z = (63.75 - 56.2) / 3.3 = 2.27

Now, we can look up the probability corresponding to a z-score of 2.27 on the standard normal distribution table. The probability is approximately 0.9883.