Question

Adult females in the US have normally distributed diastolic blood pressures with mean μ = 77 mm Hg and standard deviation σ = 11.6 mm Hg. Use this information to answer the following questions:

(a) 95% of adult females have diastolic pressures in what range? Enter the answer as an interval.(Use the 68-95-99.5 Rule)

(b) Sophia’s diastolic blood pressure is 68. What is the z-score of this value? (Use The formula for z-score)

(c) If we choose a woman at random, how likely is it that her diastolic blood pressure is between 70 and 80 mm Hg?(Use the normalcdf function on your calculator)

(d) “Hypertension” is indicated by a diastolic blood pressure over 90 mm Hg. What percentage of women have diastolic blood pressure more than 90 mm Hg?

Answer 1

= 77

= 11.6

By 68 -95-99.5 Rule:

95% of data fall within 2 standard deviation frommean.

So, range is given by:

77 (2 X 11.6)

= 77 23.2

= (53.8,100.2)

(b)
Z = (68 - 77)/11.6 = - 0.78

(c)

To find P(70 < X < 80):

Case 1: For X from 70 to mid value:

Z = (70 - 77)/11.6 = - 0.60

Area Under Standard Normal Curve = 0.2257

Case 2: For X from mid value to 80:

Z = (80 - 77)/11.6 = 0.26

Area Under Standard Normal Curve = 0.1026

So,

P(70< X < 80) = 0.2267 + 0.1026 = 0.3293

(d)

To find P(X>90):
Z = (90 - 77)/11.6 = 1.12

Area Under Standard Normal Curve = 0.3686

So,

P(X>90) = 0.5 - .3686 = 0.1314 = 13.14 %