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:
[tex]\sqrt{V(X)} = \sqrt{np(1-p)}[/tex]
9.2% of all Connecticut residents have Type B blood.
This means that [tex]p = 0.092[/tex]
A random sample of 18 Connecticut residents is taken.
This means that [tex]n = 18[/tex]
What is the standard deviation of the random variable X?
[tex]\sqrt{V(X)} = \sqrt{18*0.092*0.908} = 1.23[/tex]
The standard deviation of the random variable X is 1.23.
