# 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

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C(14, 4)*p^4*(1-p)^10=14!/(10!*4!)*0.20^4*(1-0.20)^10

=0.1720

Note: C(14, 4) is the binomial coefficient: 14 chooses 4.

D) The probability of at least 5 sets being tuned to CSI.

It is equal to

1-C(14, 0)*p^0*(1-p)^14-C(14, 1)*p*(1-p)^13-C(14, 2)*p^2*(1-p)^12

-C(14, 3)*p^3*(1-p)^11- C(14, 4)*p^4*(1-p)^10

=1-C(14, ...