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A federal study reported that 7.5 percent of the U.S.
Chapter 6, Problem 41E(choose chapter or problem)
Problem 41E
A federal study reported that 7.5 percent of the U.S. workforce has a drug problem. A drug enforcement official for the State of Indiana wished to investigate this statement. In her sample of 20 employed workers:
a. How many would you expect to have a drug problem? What is the standard deviation?
b. What is the likelihood that none of the workers sampled has a drug problem?
c. What is the likelihood at least one has a drug problem?
Questions & Answers
QUESTION:
Problem 41E
A federal study reported that 7.5 percent of the U.S. workforce has a drug problem. A drug enforcement official for the State of Indiana wished to investigate this statement. In her sample of 20 employed workers:
a. How many would you expect to have a drug problem? What is the standard deviation?
b. What is the likelihood that none of the workers sampled has a drug problem?
c. What is the likelihood at least one has a drug problem?
ANSWER:
Solution 41E
Step1 of 4:
Let us consider a random variable ‘X’ it presents the U.S. workforce has a drug problem. Also, we have ‘n = 20 and ’.
Here our goal is:
a). We need to find the expected number of a drug problem. Also, the standard deviation.
b). We need to find the likelihood that none of the workers sampled has a drug problem.
c). We need to find the likelihood at least one has a drug problem.
Step2 of 4:
a).
We know that ‘x’ follows a binomial distribution with parameters ‘n = 20 and ’. Then, the probability mass function of the binomial distribution is:
The mean of the binomial distribution is: