Question

In a recent study, the Centers for Disease Control and Prevention reported that diastolic blood pressures of adult women in the United States are approximately normally distributed with mean 80.1 and standard deviation of 9.9.

(a) Find the 70th percentile of the blood pressures.

(b) Find the 33rd percentile of the blood pressures.

(c) Find the third quartile of the blood pressures.

Use the TI-84 Plus calculator and round the answers to at least two decimal places.

Answer 1

Solution:

Given, X follows Normal distribution with,

   = 80.1

= 9.9

a)

Use the TI-84 Plus calculator.

Press 2nd and then press VARS.

Go to invnorm(

invnorm(probability , , )

For 70th percentile , probability is 0.70

invnorm(0.70 , 80.1 , 9.9)

= 85.29

b)

33rd percentile

invnorm(0.33 , 80.1 , 9.9)

= 75.74

c)

For third quartile Q₃,

P(X < Q₃) = 3/4 = 0.75

So , third quartile is given by

invnorm(0.75 , 80.1 , 9.9)

= 86.78