Question

At Aalten Technologies, bottlenecks in the assembly line occur according to a Poisson process with an average of 0.50 bottlenecks per hour of operating time. Give answers either as decimals to nearest .001 or as a simple, exact expressions involving e:

Answer 1

Probability (at least one bottle neck occurs during 8 hours of operation) = 0.9817

Step-by-step explanation:

Given:

Average bottleneck 1 hour = 0.5

Find:

Probability (at least one bottle neck occurs during 8 hours of operation)

Computation:

Expected events in 8 hour = 8(0.5)

Expected events in 8 hour = 4

Probability (at least one bottle neck occurs during 8 hours of operation) = p(X≥1)

Probability (at least one bottle neck occurs during 8 hours of operation) = 1-p(X=0)

Probability (at least one bottle neck occurs during 8 hours of operation) =1-exp(-4)[4⁰]/0!

Probability (at least one bottle neck occurs during 8 hours of operation) =1-0.0183

Probability (at least one bottle neck occurs during 8 hours of operation) = 0.9817