Question

According to a genetic theory, there is a 10% chance that a randomly selected person from a large population has a given gene. I plan to take a simple random sample of 500 people from this population. Construct a box model for the percentage of people in the sample with this gene.

a. The number of draws is ____________________.

b. The average of the tickets in the box is ____________________.

c. The SD of the tickets in the box is ____________________.

Answer 1

Given

In a genetic theory, there is a 10% chance that a randomly selected person from a large population has a given gene. i.e. p=0.10=10%

We take a simple random sample of 500 people from this population. i.e n=500

X~Binomial(n=500,p=0.10)

Mean=E(X)=np=500*0.10=50

Variance=V(X)=np(1-p)=500*0.10*(1-0.10)=45

a. The number of draws is 500.

b. The average of the tickets in the box is 50.

c. The SD of the tickets in the box is a. The number of draws is 6.70820393