# Probability: Expected Profit and Poisson Distribution

1) A contractor is considering a project which he estimates will yield a $160,000 profit with a probability of 65% and a loss of $50,000 with a 35% probability due to poor weather and material issues. What is his expected (value) profit?

2) CSI has a 20 share meaning that while it is being broadcast, 20% of the TV sets are tuned to CSI. A focus group consisting of 14 randomly selected households(each with 1 TV set), find the following for such groups of 14:

A) The mean number of TV sets tuned to CSI

B) The variance and standard deviation for TV sets tuned to CSI

C) What is the probability of exactly 4 TV sets being tuned to CSI

D) What is the probability of at least 5 sets being tuned to CSI.

3) Currently an average of 11 residents of Mooseport die each year from a population of 935. Use the Poisson Distribution formula to:

A) Find the mean number of deaths per day

B) Find the probability that on a given day there are no deaths.

C) Find the probability that on a given day, there is exactly 1 death.

D)Find the probability that on a given day, there is more than 1 death.

#### Solution Preview

1) Let X be the profit. We have the following

P(X=160,000)=0.65 and P(X=-50,000)=0.35

So,

E(X)=160000*0.65+(-50000)*0.35=$86,500

So, his expected (value) profit is $86,500.

2A) The mean number of TV sets tuned to CSI

It is equal to

np =14* 0.20= 2.8

B) The variance and standard deviation for TV sets tuned to CSI

It is equal to

np(1-p)=14*0.20*(1-0.20)=2.24

C) The probability of exactly 4 TV sets being tuned to CSI

It is equal ...

#### Solution Summary

Various probability questions are solved. The expected profits and Poisson Distributions are determined.