A small life insurance company has determined that on the average it receives 6

ID: 3045915 • Letter: A

Question

A small life insurance company has determined that on the average it receives 6 death claims per day. Assuming a Poisson distribution,

a. Find the probability that the company receives seven death claims on a randomly selected day.

b. Find the probability that the company receives at most seven death claims on a randomly selected day. c

. Find the probability that the company receives at least eight death claims on a randomly selected day.

d. Find the probability that the company receives 33 death claims on a randomly selected 5-day work week.

Solution:-

= 6

a) The probability that the company receives seven death claims on a randomly selected day is 0.1377.

x = 7

By applying poisons distribution:-

P(x; ) = (e-) (x) / x!

P(x = 7) = 0.1377

b) The probability that the company receives at most seven death claims on a randomly selected day is 0.744.

x = 7

By applying poisons distribution:-

P(x; ) = (e-) (x) / x!

P(x < 7) = 0.744

c) The probability that the company receives at least eight death claims on a randomly selected day is 0.256.

x = 8

By applying poisons distribution:-

P(x; ) = (e-) (x) / x!

P(x > 8) = 0.256

d) The probability that the company receives 33 death claims on a randomly selected 5-day work week is 0.0599.

= 6 × 5 = 30

x = 33

By applying poisons distribution:-

P(x; ) = (e-) (x) / x!

P(x = 33) = 0.0599

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.