Question

19. The National Health and Nutrition Survey reported that 39% of adults in the United States

have hypertension (high blood pressure). A sample of 24 adults is studied.

A. What is the probability that exactly 17 of them have hypertension? ____________

B. What is the probability that at least 10 of them have hypertension? ____________

C. What is the probability that at most 12 of them have hypertension? ____________

D. Would it be unusual if more than 8 had hypertension? Write your answer by using a

complete sentence or two

Answer 1

A. P(x=17) = 0.00121

B. P(x=10) = 0.15768

C. P(x=12)=0.0888

D. No , x can take any value more than 8

complete sentence or two

Explanation:

Here n= 24 ; p= 0.39 ; q = 1-0.39= 0.71

Applying binomial probability distribution

P(X=x) = nCx p^x q^n-x

Part A.

P(x=17) = 24c17 p ^17 q^24-17

P(x=17) = 0.00121510493

Part B.

P(x=10) = 24c10 p ^10 q^24-10

P(x=10) = 0.1576877824

Part C.

P(x=12) = 24c12 p ^12 q^24-12

P(x=12)=0.08887201897

D. The random variable X can obviously take on anyone of the (n+1) integer value 0,1,23,-------,n in the binomial probability distribution

where

the trials are fixed

and the successes and failures are independent.