A onthejob injury occurs once every 8 days on average at an

A on-the-job injury occurs once every 8 days on average at an automobile plant. What is the probability that the next on the job injury will occur within 10 days 5 days 1 day

Solution

injury occurs once every 8 days on average
a)
10 days injury rate is 10/8 = 1.25
P( X = 1 ) = e ^-1.25 * 1.25^1 / 1! = 0.3581
b)
5 days injury rate is 5/8 = 0.625
P( X = 1 ) = e ^-0.625 * 0.625^1 / 1! = 0.3345
c)
1 days injury rate is 1/8 = 0.625
P( X = 1 ) = e ^-0.125 * 0.125^1 / 1! = 0.1103