Question

a medical study a researcher wishes to select people in the middle 95% of the population based on blood pressure. if the mean systolic pressure is 120 and the standard deviation of the population is 8. Find the upper and lower readings that would qualify people to participate in the study. Assume the blood pressure are normally distributed

Answer 1

Solution:-

Given that,

mean = = 120

standard deviation = = 8

Using standard normal table,

P( -z < Z < z) = 95%

= P(Z < z) - P(Z <-z ) = 0.95

= 2P(Z < z) - 1 = 0.95

= 2P(Z < z) = 1 + 0.95

= P(Z < z) = 1.95 / 2

= P(Z < z) = 0.975

= P(Z < 1.96) = 0.975

= z  ± 1.96

Using z-score formula,

x = z * +

x = - 1.96 * 8 + 120

x = 104.32

Using z-score formula,

x = z * +

x = 1.96 * 8 + 120

x = 135.68

The middle 95% are from 104.32 to 135.68