Question

The systolic blood pressure of a group of​ 18-year-old women is normally distributed with a mean of 112 mmhg and a standard deviation of 11 mmhg. what percentage of​ 18-year-old women in this group have a systolic blood pressure that lies within 3 standard deviations to either side of the​ mean?

Answer 1

By the empirical rule, 99.7 percent of all values in a normal distribution lie within 3 standard deviations of the mean. Since the population is normally distributed, the percentage that lies within 3 standard deviations of the mean is 99.7 percent.

Alternatively, you can use a z-score table to look up the area between -infinity and -3 to get the percentage that lies below 3 standard deviations below the mean, and the rest of the calculations should be trivial.