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 80.6 and standard deviation 10. (a) Find the 10th percentile of the blood pressures. (b) Find the 34th 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

Answer:

A.) 67.78

B.) 76.48

C.) 87.34

Step-by-step explanation:

Given that:

Mean (m) = 80.6

Standard deviation (σ) = 10

A.) 10th percentile :

10th percentile corresponds to a Zscore of - 1.282

Zscore = (x - m) / σ

-1.282 = (x - 80.6) / 10

-12.82 = x - 80.6

x = -12.82 + 80.6

x = 67.78

B.)34th percentile of blood pressure ;

34th percentile corresponds to a Zscore of - 0.412

Zscore = (x - m) / σ

-0.412 = (x - 80.6) / 10

-4.12 = x - 80.6

x = - 4.12 + 80.6

x = 76.48

C.) third quartile = 75% = 0.75

75th percentile corresponds to a Zscore of 0.674

Zscore = (x - m) / σ

0.674 = (x - 80.6) / 10

6.74 = x - 80.6

x = 6.74 + 80.6

x = 87.34