Question

The Normal model N(69, 3) describes the distribution of male heights in the United States. Which of the following questions asks for a probability, and which asks for a measurement? Identify the type of problem and then answer the given question.

a. To be a member of the Tall Club of Silicon Valley a man must be at least 74 inches tall. What percentage of men would qualify for membership in this club?

b. Suppose the Tall Club of Silicon Valley wanted to admit the tallest 2% of men. What minimum height requirement should the club set for its membership criteria?

Answer 1

The question asks for a probability and a measurement. To find the probability, calculate the percentage of men taller than a certain height using the Normal model. To find the measurement, determine the minimum height requirement based on a given percentage.

Step-by-step explanation:

The question asks for a probability when it asks, 'What percentage of men would qualify for membership in this club?' To find this probability, we can use the Normal model N(69, 3) to calculate the percentage of men taller than 74 inches. We can find this by calculating the area under the curve to the right of 74 inches.

On the other hand, the question asks for a measurement when it asks, 'What minimum height requirement should the club set for its membership criteria?' This requires finding the height value that corresponds to the top 2% of men, which can be done using the Z-table for the Normal distribution.