Question

Mean and Standard Deviation of Senior Citizens In the 2010 US Census, we learn that of all people in the US are senior citizens. Let the random variable X represent the number of senior citizens in a random sample of 9 people. Find the mean and standard deviation of this random variable. Enter the exact answer for the mean, and round your answer for the standard deviation to three decimal places.

Answer 1

The mean of X is 1.17.

The standard deviation of X is 1.009.

Explanation:

The question is incomplete: 1ean and Standard Deviation of Senior Citizens In the 2010 US Census, we learn that of all people in the US 13% are senior citizens. Let the random variable X represent the number of senior citizens in a random sample of 9 people. Find the mean and standard deviation of this random variable. Enter the exact answer for the mean, and round your answer for the standard deviation to three decimal places.

This variable X can be modeled as a binomial random variable, with n=9 and p=0.13.

The mean of X is:

`\mu=np=9*0.13=1.17`

The standard deviation of X is:

`\sigma=√(npq)=√(9*0.13*0.87)=√(1.0179)=1.009`