Homework SourseThe National Safety Council NSC estimates that off the job a
The National Safety Council (NSC) estimates that off the job accidents cost US businesses almost $200 billion annually in lost productivity. Based on NSC estimates, companies with 50 employees are expected to average three employee off the job accidents per year. Answer the following questions for companies with 50 employees. A. What is the probability of no off the job accidents during a one year period? B. What is the probability of at least two off the job accidents during a one year period? C. What is the expected number of off the job accidents during six months? D. What is the probability of no off the job accidents during the next six months?
Solution
a)
Note that the probability of x successes out of n trials is
P(x) = u^x e^(-u) / x!
where
u = the mean number of successes = 3
x = the number of successes = 0
Thus, the probability is
P ( 0 ) = 0.049787068 [ANSWER]
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b)
Note that P(at least x) = 1 - P(at most x - 1).
Using a cumulative poisson distribution table or technology, matching
u = the mean number of successes = 3
x = our critical value of successes = 2
Then the cumulative probability of P(at most x - 1) from a table/technology is
P(at most 1 ) = 0.199148273
Thus, the probability of at least 2 successes is
P(at least 2 ) = 0.800851727 [ANSWER]
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c)
6 months is half a year, so we expect
E(x) = 3*(1/2) = 3/2 or 1.5 [ANSWER]
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d)
Note that the probability of x successes out of n trials is
P(x) = u^x e^(-u) / x!
where
u = the mean number of successes = 1.5
x = the number of successes = 0
Thus, the probability is
P ( 0 ) = 0.22313016 [ANSWER]
