Question

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

Answer 1

Answer:

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

Answer 2

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

A. $P(X = 40) = C_{50,40}(0.31)^{40}(0.69)^{10}$

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

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

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

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.

In this problem:

• Sample of 50 residents, hence $n = 50$
• 31% have a bachelor's degree, hence $p = 0.31$

Hence, the probability that B will equal 40 is:

A. $P(X = 40) = C_{50,40}(0.31)^{40}(0.69)^{10}$

A similar problem is given at https://brainly.com/question/19977321