Network breakdowns are unexpected rare events that occur every 3 weeks, on the average. compute the probability of more than 4 breakdowns during a 21-week period

0.827

Step-by-step explanation:

Data provided in the question:

Probability of breakdown, p = once in 3 weeks i.e

number of weeks n = 21

now,

mean, λ = np

=  

= 7

P(X > 4) = 1 - ( P(X ≤ 4))

using Poisson distribution

P(X = x) =

Thus,

P(X = 0) =

= 0.00091

P(X = 1) =

= 0.00638

P(X = 2) =

= 0.02234

P(X = 3) =

= 0.05213

P(X = 4) =

= 0.09123

Thus,

P(X ≤ 4) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4)

= 0.00091 + 0.00638 + 0.02234 + 0.05213 + 0.09123

= 0.17299

Therefore,

P(X > 4) = 1 - 0.17299

= 0.827

answer: city needs 2.4 inches of rainfall more to match the record of 40 inches.

step-by-step explanation:

since we have given that

total annual rainfall a city record = 40 inches

this year, total rainfall recorded = 37.6 inches

number of inches of rainfall   is needed to match the record of 40 inches is given by

hence, city needs 2.4 inches of rainfall more to match the record of 40 inches.