. Find the probability that his height is less than 66 inches. .Find the probability that his height is between 66 and 72 inches. . Find the probability that his height is more than 72 inches.

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**Statistics Exercise - Calculating Probability and Z-Scores**

**Problem 4: Height Distribution of U.S. Men**

A survey was conducted to measure the height of U.S. men. In the survey, respondents were grouped by age. In the 20-29 age group, the heights were normally distributed, with a mean of 68.6 inches and a standard deviation of 3 inches. A study participant is randomly selected.

a. **Find the probability that his height is less than 66 inches.**

b. **Find the probability that his height is between 66 and 72 inches.**

c. **Find the probability that his height is more than 72 inches.**

**Problem 5: Z-Score Calculation**

For Problem 5, find the indicated z-score and sketch the curve.

5. **Find the z-score for which 80% of the distribution's area lies between -z and z.**

*Graph/Diagram Explanation:*

The normal distribution curve is characterized by its bell shape, with the mean at the center. In these problems, the mean height (68.6 inches) would be at the center of the x-axis on the graph, and the standard deviations would help in determining the spread of the curve. In Problem 5, you would sketch a standard normal distribution curve where the desired z-scores encapsulate 80% of the area under the curve centered around the mean, with 10% of the distribution in each tail.
Transcribed Image Text:**Statistics Exercise - Calculating Probability and Z-Scores** **Problem 4: Height Distribution of U.S. Men** A survey was conducted to measure the height of U.S. men. In the survey, respondents were grouped by age. In the 20-29 age group, the heights were normally distributed, with a mean of 68.6 inches and a standard deviation of 3 inches. A study participant is randomly selected. a. **Find the probability that his height is less than 66 inches.** b. **Find the probability that his height is between 66 and 72 inches.** c. **Find the probability that his height is more than 72 inches.** **Problem 5: Z-Score Calculation** For Problem 5, find the indicated z-score and sketch the curve. 5. **Find the z-score for which 80% of the distribution's area lies between -z and z.** *Graph/Diagram Explanation:* The normal distribution curve is characterized by its bell shape, with the mean at the center. In these problems, the mean height (68.6 inches) would be at the center of the x-axis on the graph, and the standard deviations would help in determining the spread of the curve. In Problem 5, you would sketch a standard normal distribution curve where the desired z-scores encapsulate 80% of the area under the curve centered around the mean, with 10% of the distribution in each tail.
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