Answer:
a) The expected number is 5.
b) 0.25% probability that none of the workers say they will burn out in the near future
c) 97.93% probability that at least two of the workers say they will burn out in the near future
Step-by-step explanation:
For each person, there are only two possible outcomes. Either they said they will burnout in the near future, or they did not. The probability of a person saying that they will burnout in the near future is independent of any other person. So the binomial probability distribution is used to solve this question.
Binomial probability distribution
The binomial probability is the probability of exactly x successes on n repeated trials, and X can only have two outcomes.
In which 
is the number of different combinations of x objects from a set of n elements, given by the following formula.
And p is the probability of X happening.
33 % said they expected to burn out in the job in the near future.
This means that 
15 workers
This means that 
a. Suppose a random sample of 15 American workers is selected. What is the expected number of these sampled workers who say they will burn out in the near future?
The expected number of the binomial distribution is given by the following formula:
So
The expected number is 5.
b. What is the probability that none of the workers say they will burn out in the near future?
This is P(X = 0).
0.25% probability that none of the workers say they will burn out in the near future
c. What is the probability that at least two of the workers say they will burn out in the near future?
Either less than two say this, or at least two do. The sum of the probabilities of these events is decimal 1. So
We want 
. So
In which
97.93% probability that at least two of the workers say they will burn out in the near future
