Question

According to data from the CDC, about 37.1% of adults (individuals 18 years of age or older) in the United States and 57.9% of children (individuals between 6 months and 17 years of age) in the United States received a flu vaccine during the 2017-2018 flu season.



a) Consider a random sample of 50 adults.



i. Calculate the probability that exactly 20 adults received a flu vaccine.

Answer 1

Using the binomial distribution, there is a 0.1094 = 10.94% probability that exactly 20 adults received a flu vaccine.

For each adult, there are only two possible outcomes, either they received the vaccine or they did not. The probability of an adult receiving the vaccine is independent of any other adult, hence the binomial distribution is used to solve this question.

What is the binomial distribution formula?

The formula is:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$C_{n,x} = \frac{n!}{x!(n-x)!}$

The parameters are:

• x is the number of successes.

• n is the number of trials.

• p is the probability of a success on a single trial.

For this problem, we have that:

• There is a random sample of 50 adults, hence n = 50.

• 37.1% of adults received the flu vaccine, hence p = 0.371.

The probability that exactly 20 adults received a flu vaccine is P(X = 20), hence:

$P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}$

$P(X = 20) = C_{50,20}.(0.371)^{20}.(0.629)^{30} = 0.1094$

0.1094 = 10.94% probability that exactly 20 adults received a flu vaccine.

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

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