A research study uses 800 men under the age of 55. Suppose

Chapter 3, Problem 145E

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QUESTION:

Problem 145E

A research study uses 800 men under the age of 55. Suppose that 30% carry a marker on the male chromosome that indicates an increased risk for high blood pressure.

(a) If 10 men are selected randomly and tested for the marker, what is the probability that exactly 1 man has the marker?

(b) If 10 men are selected randomly and tested for the marker, what is the probability that more than 1 has the marker?

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QUESTION:

Problem 145E

A research study uses 800 men under the age of 55. Suppose that 30% carry a marker on the male chromosome that indicates an increased risk for high blood pressure.

(a) If 10 men are selected randomly and tested for the marker, what is the probability that exactly 1 man has the marker?

(b) If 10 men are selected randomly and tested for the marker, what is the probability that more than 1 has the marker?

ANSWER:

Solution :

Step 1 of 2:

Given study says 30% of 800 men shows marker.

Let X denote the number of men who carry marker in the sample.

Let X follows Hypergeometric with parameters N, n, and k.

The probability mass function is

f(x)= P(X=x)

P(X=x) =

Where,

N = population size =800

n = sample size = 10

Here the number men classified as a success is k.

k= 

k= 240

Our goal is:

a). We need to find the probability that exactly 1 man has the marker.

b). We need to find the probability that more than 1 man has the marker.

a). Given if we randomly selected 10 men and tested for the marker.

Then the probability that exactly 1 man has the marker is

P(X=1) =  

P(X=1) =

P(X=1) =

P(X=1) = 0.12007

Therefore, the probability that exactly 1 man has the marker is 0.12007.


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