Question

The blood pressure in millimeters was measured for a large sample of people. The average pressure is 140 mm, and the SD of the measurements is 20 mm. The histogram looks reasonably like a normal curve. Use the normal curve to estimate the following percentages. Choose the answer that is closest to being correct.

a. 10.6%
b. 89.4%
c. 39.4%
d. 78.8%
e. 68.27%

___ The percentage of people with blood pressure between 115 and 165 mm.
___ The percentage of people with blood pressure between 140 and 165 mm.
___ The percentage of people with blood pressure over 165 mm.

Answer 1

Kindly check explanation

Explanation:

Given the following :

Assum a normal distribution :

Mean (m) = 140 mm

Standard deviation (sd) = 20 mm

The percentage of people with blood pressure between 115 and 165 mm.

Zscore = (x - m) / sd

X = 115 mm

(115 - 140) / 20

-25/20 = - 0.625 = - 0.63

P(z<-0.63) = 0.2643

X = 165 mm

(165 - 140) / 20

25/20 = 0.625 = 0.63

P(z< 0.63) = 0.7357

0.7357 - 0.2643 = 0.4714 = 47.14%

B.) The percentage of people with blood pressure between 140 and 165 mm.

Zscore = (x - m) / sd

X = 140 mm

(140 - 140) / 20

0/20 = 0 = 0

P(z<0) = 0.5000

X = 165 mm

(165 - 140) / 20

25/20 = 0.625 = 0.63

P(z< 0.63) = 0.7357

0.7357 - 0.5000 = 0.2357 = 23.57%

C.) ___ The percentage of people with blood pressure over 165 mm.

X = 165mm

(165 - 140) / 20

25/20 = 0.625 = 0.63

1 - P(z< 0.63) = 0.7357

1 - 0.7357 = 0.2643 * 100% = 26.43%