Question

Problem: Suppose that on-the-job injuries in textile mill occur at the rate of 0.1 per day. What is the probability that two accidents will occur during the (five-day) work week

Answer 1

Answer: the probability that two accidents will occur during the (five-day) work week is 0.0758

Step-by-step explanation:

Given that;

injuries in textile mill occur at the rate of 0.1 per day; λ = 0.1

probability that two accidents will occur during the (five-day) work week = ?

T= 5

so, the average number of on the job injuries for five days will be;

λT = 0.1 × 5

= 0.5

now if X follows Poisson distribution, hemce

P( X=k ) = [e^-λT (λT)^k] / k!

so the probability that two (2) accidents will occur during the (five-day) work week will be;

P( X=k ) = [e^-0.5 (0.5)²] / 2!

= (0.6065 × 0.25) / 2

= 0.1516/ 2

= 0.0758

the probability that two accidents will occur during the (five-day) work week is 0.0758