Question

Name: MTH 220 HW 1B Total Points: 20 X-NOM, 1. The blood pressure of a female in the United States is normally distributed with mean 123 and a standard deviation of 16. (10 points) a. What is the probability that a randomly chosen female has a blood pressure over 1627 M=123 -16 P(Z >162)- z = x b. Normal blood pressure reading is considered to be between 120 and 140. What is the probability that a randomly chosen female has normal blood pressure? P(120424140) Tua c. What blood pressure would put a female in the top 10% of the population?

Answer 1

Answer)

As the data is normally distributed we can use standard normal z table to estimate the answers

Z = (x-mean)/s.d

Given mean = 123

S.d = 16

A)

P(x>162)

Z = (162 - 123)/16 = 2.44

From z table, P(z>2.44) = 0.0073

B)

P(120<x<140) = P(x<140) - P(x<120)

P(x<140)

Z = (140 - 123)/16 = 1.06

From z table, P(z<1.06) = 0.8554

P(x<120)

Z = -0.19

From z table, P(z<-0.19) = 0.4247

Required probability is 0.8554 - 0.4247 = 0.4307

C)

From z table, P(z>1.28) = 10%

1.28 = (x - 123)/16

X = 143.48