According to a study, nearly 80% of workers in law libraries are satisfied with their job. Assume the true proportion of law librarians are satisfied with their job is 0.8. In a random sample of 20 law librarians, what is the probability that at most 4 are unsatisfied with their job?

0.618

Step-by-step explanation:

This is a binomial distribution. We are to determine the probability of people unsatisfied. If we denote the probability of being satisfied with , then . Let be the probability of being unsatisfied. Then

Since the random sample is 20 and is small enough, we can use the Poisson probability function

where is the mean and is given by .

Denoting the probability of at most 4 unsatisfied with ,

what is the original number? you forgot to add it.

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)