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