Elementary Statistics

Question 1:
A poll is taken in a town, with the following results:

Democrat     Republican     Independent
Male    50    60    50
Female    40    40    60

Suppose a random voter is chosen from this town. Let A = the event that the voter is a Democrat, and B = the event that the voter is female. Find the following Probabilities:

a.    P (A)
b.    P (B)
c.    P (not A)
d.    P (A and B)
e.    P (A or B)
f.    P (A¦B)
g.    Are A and B mutually exclusive events? Why or why not?
h.    Are A and B independent events? Why or why not?

Question 2:
An insurance company offers to sell you a life insurance policy which will pay your beneficiary $100.000 if you die. They estimate that the probability that you will die in the next year is 0.00086. If the company wants to expert to make a profit on the policy, then how much do they have to charge per year?

Question 3:
A basketball player makes 82% of her free throw attempts. Suppose she takes 20 free and we let X = the number of free throws that she makes.
a.    What are the possible values for X?
b.    What is the mean and standard deviation for X?
c.    Find P (X = 15).
d.    Find P (X = 15).
e.    Find P (10 = X = 18).

Question 4:
A fuel economy for a model of car is normally distributed with mean 26 mpg (miles per gallon) and standard deviation 4 mpg. One of these cars is selected at random, and we let X = that cars fuel economy.
a.    Find P (22 = X = 28).
b.    Find P (X = 30).
c.    How many miles per gallon do the top 7% of these cars get?

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