Question

According to the American Community Survey, 27% of residents of the United States 25 years old or older had earned a bachelor degree. Suppose you select 12 residents of the United States 25 years old or older and recorded the number who had earned a bachelor degree. Round probabilities to 4 decimal places.
Explain why this is a binomial experiment.

Find and interpret the probability that exactly 5 of them had a bachelor degree.

Find and interpret the probability that fewer than 5 of them had a bachelor degree.

Find and interpret the probability that at least 5 of them had a bachelor degree.

Compute the mean and standard deviation of the binomial random variable.

Answer 1

a. The reason why this question is a binomial experiment is based on the fact that it is made up of an independent sample, it has a number that is fixed and a probability.

Each event is made up of two outcomes and they are random with the same success rate.

b. How to solve probability that exactly 5 had a bachelor

we have the following data n = 12, p = 0.27 and k = 5

We have to use the function to solve electronically

binompdf(n,p,k)

input the values

= binompdf(12,0.27,5)

This gives us

= 0.1255

(C) Probability that fewer than 5 have bachelor

We use the formula below

= binompdf(12,0.27,5-1)

This is = 0.7984

D. Probability of at least 5

1 - probability of fewer than 5

= 1 - 0.7984

= 0.2016

How to solve for the Mean = n*p

n = 12 , p = 0.27

Mean = 12*0.27 = 3.24

and

standard deviation = √npq

n = 12, p = 0.27 , q = 1- 0.27

= 0.73

sd = √12*.27*.73

= 1.54

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