Question

According to the American Red Cross, 9.2% of all Connecticut residents have Type B blood. A random sample of 18 Connecticut residents is taken. What is the standard deviation of the random variable X?

Answer 1

Answer:

The standard deviation of the random variable X is 1.23.

Step-by-step explanation:

For each Connecticut resident, there are only two possible outcomes. Either they have Type B blood, or they do not. The probability of a resident having type B blood is independent of other residents. So we use the binomial probability distribution to solve this question.

Binomial probability distribution

Probability of exactly x sucesses on n repeated trials, with p probability.

The standard deviation of the binomial distribution is:

$\sqrt{V(X)} = \sqrt{np(1-p)}$

9.2% of all Connecticut residents have Type B blood.

This means that $p = 0.092$

A random sample of 18 Connecticut residents is taken.

This means that $n = 18$

What is the standard deviation of the random variable X?

$\sqrt{V(X)} = \sqrt{18*0.092*0.908} = 1.23$

The standard deviation of the random variable X is 1.23.