1 The National Safety Council NSC estimates that offthejob a

1.  The National Safety Council (NSC) estimates that off-the-job accidents cost U.S. businesses almost $200 billion annually in lost productivity (National Safety Council, March 2006). Based on NSC estimates, companies with 50 employees are expected to average 3 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

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

a)
P( X = 0 ) = ( 50 0 ) * ( 0.06^0) * ( 1 - 0.06 )^50
= 0.0453

b)

P( X < 2) = P(X=1) + P(X=0) +
= ( 50 1 ) * 0.06^1 * ( 1- 0.06 ) ^49 + ( 50 0 ) * 0.06^0 * ( 1- 0.06 ) ^50 +   
= 0.19
P( X > = 2 ) = 1 - P( X < 2) = 0.81