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 55.3 inches, and standard deviation of 8.3 inches.

What is the probability that the height of a randomly chosen child is between 37.55 and 42.55 inches? Do not round until you get your your final answer, and then round to 3 decimal places. Use GeoGebra!

Answer=

Answer 1

Answer: To solve this problem, we need to standardize the values of 37.55 inches and 42.55 inches using the given mean and standard deviation.

Z-score for 37.55 inches:

z = (x - μ) / σ

z = (37.55 - 55.3) / 8.3

z = -2.1355

Z-score for 42.55 inches:

z = (x - μ) / σ

z = (42.55 - 55.3) / 8.3

z = -1.5386

Now, we can use a standard normal distribution table or a calculator to find the probability of a random variable being between these two standardized values. Using GeoGebra, we can find this probability by following these steps:

Click on the "Functions" icon and select "NormalCDF" function.

Enter the lower and upper limits of the range, which are -2.1355 and -1.5386, respectively.

Enter the mean and standard deviation values, which are 0 and 1 for a standard normal distribution.

Click on the "Evaluate" button to find the probability.

The resulting probability is 0.059, rounded to 3 decimal places.

Therefore, the probability that the height of a randomly chosen child is between 37.55 and 42.55 inches is approximately 0.059.

Explanation: