Question

Twenty percent of adults in a particular community have at least a​ bachelor's degree. Suppose x is a binomial random variable that counts the number of adults with at least a​ bachelor's degree in a random sample of 100 adults from the community. If you are using a calculator with the binompdf and binomcdf​ commands, which of the following is the most efficient way to calculate the probability that more than 60 adults have a​ bachelor's degree, ​P(x?>60)?

a. P(x < 60)=binompdf(100,0 20,59)
b. P(x<60)=binompdf(100.0.20.60)
c. P(x<60)= binomcdf(100,0,20,59)
d. P(x<60)=binomcdf (100.0.20.60)

Answer 1

Explanation:

Since x is a binomial random variable that counts the number of adults with at least a bachelor's degree, it means that there are only two outcome. It is either an adult has a bachelor's degree or not. The probability of success would be that the adult has a bachelor's degree. Therefore, probability of success, p = 20/100 = 0.2

Number of adults in the sample is 100

The number of success expected is x

We want to determine the probability of P(x ≥ 60)

Therefore, the most efficient way to calculate the probability that more than 60 adults have a bachelor's degree is

b. P(x<60)=binompdf(100.0.20.60)

This is because it is a discrete probability distribution function