Question

What is the probability that the woman has a diastolic blood pressure between 60 and 90 mmHg?

1. Suppose you have a variable X~N(8, 1.5).

Among females in the US between 18 and 74 years of age, diastolic blood pressure is normally distributed with mean µ=77mmHg and standard deviation σ=11.6mmHg

Note- 0.87 was not correct

Answer 1

Solution:

We are given that: Among females in the US between 18 and 74 years of age, diastolic blood pressure is normally distributed with mean µ =77mmHg and standard deviation σ =11.6mmHg

We have to find: the probability that the woman has a diastolic blood pressure between 60 and 90 mmHg

That is: We have to find:

P( 60 < X < 90) = .............?

Thus find z score for x = 60 and for x = 90

z score formula is:

and

Thus we get:

P( 60 < X < 90) = P( -1.47 < Z < 1.12)

P( 60 < X < 90) = P( Z < 1.12) - P( Z < -1.47)

Look in z table for z = -1.4 and 0.07 as well as for z = 1.1 and 0.02 and find area.

P( Z < -1.47) = 0.0708

P( Z < 1.12) = 0.8686

Thus we get:

P( 60 < X < 90) = P( Z < 1.12) - P( Z < -1.47)

P( 60 < X < 90) = 0.8686 - 0.0708

P( 60 < X < 90) = 0.7978