Question

An insurance company study shows that 9% of U. S. adults have diabetes. Suppose 8 US adults are selected at random. LetX be the number of US adults among the 8 selected that have diabetes. Find the mean and standard deviation of X.

Answer 1

Using the binomial distribution, it is found that:

• The mean of X is of 0.72.

• The standard deviation of X is of 0.81.

What is the binomial probability distribution?

It is the probability of exactly x successes on n repeated trials, with p probability of a success on each trial.

The expected value of the binomial distribution is:

E(X) = np

The standard deviation of the binomial distribution is:

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

For this problem, the parameters are given as follows:

n = 8, p = 0.09.

Hence the mean and the standard deviation are, respectively:

• E(X) = np = 8 x 0.09 = 0.72.

• $\sqrt{V(X)} = \sqrt{np(1-p)} = \sqrt{8 \times 0.09 \times 0.91} = 0.81$

More can be learned about the binomial distribution at brainly.com/question/24863377

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