Question

Use the empirical rule to solve the following problems below (DO NOT use the online calculators to solve these problems) Assume all the data follow the normal distribution:

1. The average height of males in a certain population is 68 inches, with a standard deviation of 3 inches. What percentage of the males in that population are between 62 and 74 inches tall?

Answer 1

Using the empirical rule for a population with a mean height of 68 inches and a standard deviation of 3 inches, approximately 95% of males are expected to be between 62 and 74 inches tall.

Step-by-step explanation:

The empirical rule, also known as the 68-95-99.7 rule, states that for a normal distribution, approximately 68% of the data will fall within one standard deviation from the mean, 95% within two standard deviations, and 99.7% within three standard deviations. In the case of the population of male heights with an average of 68 inches and standard deviation of 3 inches, we want to find the percentage of males between 62 and 74 inches tall.

To do this, we calculate the number of standard deviations 62 and 74 inches are from the mean:

• 62 inches is 2 standard deviations below the mean (68 - 62 = 6, divided by standard deviation 3).
• 74 inches is 2 standard deviations above the mean (74 - 68 = 6, divided by standard deviation 3).

The empirical rule states that 95% of the data falls within two standard deviations from the mean, so the answer is that approximately 95% of the male population will be between 62 and 74 inches tall.