d. Compute the probability of more than one accident during a month The National
ID: 3361905 • Letter: D
Question
d. Compute the probability of more than one accident during a month The National Safety Council (NSC) estimates that off-the-job accidents cost U. nesses almost $200 billion annually in lost productivity (National Safety 2006). three employee off-the-job accidents per year. Answer the following questions for com- panies 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 51. Council, March Based on NSC estimates, companies with 50 employees are expected to average period? What is the expected number of off-the-job accidents during six months? What is the probability of no off-the-job accidents during the next six months? c. d.Explanation / Answer
The probability of off-the job accident per year, p = 3/50 = 0.06
The probability of no off-the job accident per year, 1-p = 1 - 0.06 = 0.94
Size of employees, n = 50
(a)
Probability of no off-the job accidents = 0.9450 = 0.0453
(b)
Let X denotes the number of off-the-job accidents is a year.
Probability of atleast two off-the job accidents = P(X >= 2) = 1 - [P(X=0) + P(X=1)]
= 1 - [50C0 * 0.060 * 0.9450 + 50C1 * 0.061 * 0.9449]
= 1 - [0.0453 + 0.1447] = 0.81
(c)
The expected number of off-the accidents during 1 year = 3
The expected number of off-the accidents during six months = 3 / 2 = 1.5
d.
The probability of off-the job accident during six months, p = 1.5/50 = 0.03
The probability of no off-the job accident during next six months = 1-p = 1 - 0.03 = 0.97
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