Question

For women aged 18-24, systolic blood pressures (in mm Hg) are normally distributed with a mean of 114.8 and a standard deviation of 13.1. Hypertension is commonly defined as a systolic blood pressure above 140.

a. If a woman between the ages of 18 and 24 is randomly selected, find the probability that her systolic blood pressure is greater than 140.

b. If 4 women in that age bracket are randomly selected, find the probability that their mean systolic blood pressure is greater than 140.

Answer 1

Solution :

Given that ,

a) P(x > 140) = 1 - p( x< 140)

=1- p P[(x - ) / < (140 - 114.8) / 13.1]

=1- P(z < 1.92)

= 1 - 0.9726

= 0.0274

b) = 114.8

= / n = 13.1 / 4 = 6.55

P( > 140) = 1 - P( < 140)

= 1 - P[( - ) / < (140 - 114.8) / 6.55]

= 1 - P(z < 3.85)   

= 1 - 0.9999

= 0.0001