Metal fatigue causes cracks to appear on the skin of older aircraft. Assume that for a certain year and model of aircraft the average number of cracks is 3 per 1 m2 section of aircraft. Find the probability that we observe 4 cracks when inspecting a 3 m2 section. Round to three decimal places.

Answer: the probability that we observe 4 cracks when inspecting a 3 m2 section is 0.034

Step-by-step explanation:

The formula for poisson distribution is expressed as

P (x = r) = (e^ - µ * µ^r) / r!

Where

µ represents the mean of the theoretical distribution.

r = x represents the number of successes of the event (cracks).

From the information given,

µ = 3 cracks per 1 m² section

It means that for a 3 m² section of the aircraft, the average number of cracks would be 9

the probability that we observe 4 cracks when inspecting a 3 m2 section would be

P (x = 4) = (e^ - 9 * 9^4) / 4!

P (x = 4) = 0.034