Question

The systolic blood pressure (given in millimeters) of males has an approximately normal distribution with mean 123 and standard deviation 12. Systolic blood pressure for males follows a normal distribution. The bottom 7% of men have systolic blood pressures below what value?

Answer 1

Solution:

Given, X follows Normal distribution with,

   = 123

= 12

For Bottom 7% data , let x be the required cut-off.

P(X < x) = 7% = 0.07

For the standard normal variable z , P(Z < z) = 0.84

Use z table , see where is 0.07 probability and then see the corresponding z value.

P(Z < -1.476) = 0.07

So z = -1.476

Now using z score formula ,

x = + (z * ) = 123 + (-1.476* 12) = 105.288

Required answer : 105.288