Let X be the number of failed modules in t months. Average number of modules failure per month is 1.3

Assuming X follows Poisson distribution, X ~ Poisson(\lambda = 1.3t)

For 3-month period, t = 3 and X ~ Poisson(\lambda = 1.3 * 3 = 3.9)

Probability that the maintenance crew have to go to the solar installation before the end of the regular 3-month period =

P(X > 7) = 1 - P(X \le 7)

= 1 - [P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5) + P(X = 6) + P(X = 7)]

= 1 - [exp(-3.9) * 3.90 / 0! + exp(-3.9) * 3.91 / 1! + exp(-3.9) * 3.92 ​​​​​​​/ 2! + exp(-3.9) * 3.93 ​​​​​​​/ 3! + exp(-3.9) * 3.94 ​​​​​​​/ 4! + exp(-3.9) * 3.95 ​​​​​​​/ 5! + exp(-3.9) * 3.96 ​​​​​​​/ 6! + exp(-3.9) * 3.97 ​​​​​​​/ 7! ]

= 1 - (0.02024191 + 0.07894345 + 0.15393974 + 0.20012166 + 0.19511862 + 0.15219252 + 0.09892514 + 0.05511543)

= 0.04540153