Question

Watch help video For males in a certain town, the systolic blood pressure is normally distributed with a mean of 110 and a standard deviation of 9. Using the empirical rule, determine the interval of systolic blood pressures that represent the middle 95% of males.

Answer 1

The middle 95% of males' systolic blood pressures in a certain town can be determined using the empirical rule. The interval of systolic blood pressures that represent the middle 95% of males is from 92 to 128 millimeters.

Step-by-step explanation:

The question is asking us to use the empirical rule to determine the interval of systolic blood pressures that represent the middle 95% of males in a certain town.

The empirical rule states that for a normal distribution, about 68% of the data falls within one standard deviation of the mean, about 95% falls within two standard deviations, and about 99.7% falls within three standard deviations.

Since we're looking for the middle 95% of data, that corresponds to two standard deviations on each side of the mean. So, we need to find the range that is two standard deviations below the mean and two standard deviations above the mean.

Using the formula:

Lower bound = Mean - (2 * Standard Deviation)

Upper bound = Mean + (2 * Standard Deviation)

Lower bound = 110 - (2 * 9) = 92

Upper bound = 110 + (2 * 9) = 128

Therefore, the interval of systolic blood pressures that represent the middle 95% of males in the town is from 92 to 128 millimeters.