According to a recent survey, 31 percent of the residents of a certain state who are age 25 years or older have a bachelor’s degree. A random sample of 50 residents of the state, age 25 years or older, will be selected. Let the random variable B represent the number in the sample who have a bachelor’s degree. What is the probability that B will equal 40? A. (5040)(0.31)40(0.69)10

B. (5040)(0.69)40(0.31)10

C. (4010)(0.31)40(0.69)10

D. (4010)(0.69)40(0.31)10

E. 40(0.31)50

Using the binomial distribution, it is found that the probability that B will equal 40 is:

A.

For each person, there are only two possible outcomes, either they have a bachelor's degree, or they do not. The probability of a person having a bachelor's degree is independent of any other person, which means that the binomial distribution is used to solve this question.

Binomial probability distribution

The parameters are:

In this problem:

Hence, the probability that B will equal 40 is:

A.

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A. (5040)(0.31)40(0.69)10

Step-by-step explanation:

Given. That :

P(resident who is 25 years or older) = 0.31

Sample size (n) = 50

Probability that B will be equal 40 ; r = 40

The probability that B = 40 can be obtained using the binomial probability formula :

P(x) = nCx * p^r * (1 - p)^(n - x)

Here, x = 40

P(40) = 50C40 * 0.31^40 * (1 - 0.31)^(50 - 40)

P(40) = 50C40 * 0.31^40 * 0.69^10

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step-by-step explanation: