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 55.7 inches, and standard deviation of 2.6 inches.

What is the probability that the height of a randomly chosen child is between 52.2 and 60.6 inches? Do not round until you get your your final answer, and then round to 3 decimal places.

Answer=
(Round your answer to 3 decimal places.)

Answer 1

Answer: Therefore, the probability that the height of a randomly chosen child is between 52.2 and 60.6 inches is 0.884. Rounded to 3 decimal places, the answer is 0.884.

Step-by-step explanation:We can use the standard normal distribution to find the probability that the height of a randomly chosen child is between 52.2 and 60.6 inches.

First, we need to standardize the values using the formula:

z = (x - mu) / sigma

where:

x = 52.2 and 60.6 (the values we want to find the probability between)

mu = 55.7 (the mean)

sigma = 2.6 (the standard deviation)

For x = 52.2:

z = (52.2 - 55.7) / 2.6 = -1.346

For x = 60.6:

z = (60.6 - 55.7) / 2.6 = 1.885

Next, we use a standard normal distribution table or calculator to find the area between these two z-scores:

P(-1.346 < z < 1.885) = 0.884

Therefore, the probability that the height of a randomly chosen child is between 52.2 and 60.6 inches is 0.884. Rounded to 3 decimal places, the answer is 0.884.