Question

The systolic blood pressure is normally distributed with mean of 120 and standard deviation of 16. Find

1. What is the range for 68% of the population?

2. What percent of the students would have blood pressure in the range of 88 and 152

3. What is the variance?

Answer 1

by emperical rule on normal distribution , we have

1) 68 % of data is distributed with in one standard deviation about mean .

2) 95% of data is distributed with in 2 standard deviation about mean .

a) here mean is 120 and standard deviation is 16 .

68% of population is with in 1 standard deviation . that is from 120-16= 104 to 120+16= 136 .

so range for 68% is 104 to 136

b) 88 means 120-2*16 and 152 means 120+2*16 .

so the region is with in two standard deviation about mean . so percentage is 95%

so 95% percentage with in 88 to 152

c) we know

variance= standard deviation²

so

variance= 16²= 256

so variance is 256