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Name:_________________________
Date:_______________
Period: ____ AP Statistics
Worksheet 7-1, 2
Choose an American teenager at random and let the random variable X be the number of persons that they
have kissed before graduating from high school. The probability distribution of X is as follows:
People
|
0
1
2
3
4
5
6
7+
Probability
|
.14
.18
.22
.16
.11
.09
.04
.06
1. Verify that this is a legitimate discrete probability distribution.
2. What is P( x > 5)
3. What is P( x> 5)
4. What is P( 1 < x < 4 )
5. What is the probability that a randomly chosen teenager has kissed at most two people (write in terms
of X first)?
6. What is the probability that a randomly chosen teenager has never been kissed (write in terms of X
first)?
7. Some Japanese consumers are willing to pay premium prices for Maine lobsters. One factor in the
high cost is the mortality rate during the long-distance shipping from Maine to Japan. Suppose the
number of deaths X per crate of 10 lobsters is given by the following probability distribution.
X
0
1
2
3
4
5
P( X ) 0.48 0.28 0.17 0.05 0.01 0.01
a) How many living lobsters would we expect to arrive in Japan per crate?
b) If a company makes $7.50 per lobster, how much profit would we expect from 10 crates?
c) If one restaurant wants only the lobster claws, how many claws would the shipping company
expect to lose from 3 crates?
8. Suppose X and Y are random variables with  X =175,  X =12,  Y =120,  Y =18. Given that X and
Y are independent variables, calculate the following:
 2 X Y 
 X Y 
 X Y 
 X Y 
 2X 
 X Y 
9. The random variable X denotes the number of Granny Smith apples per purchase by supermarket
shoppers in the express lane. The probability distribution is given below:
X
1
2
3
P( X ) 0.35 0.40 0.25
a) Find the expected value, variance and standard deviation for the number of apples.
b) If the apples are 50¢ each, what is the expected cost? The standard deviation of cost?
c) A shopper in the express lane is expected to spend 72¢ on bananas with a standard deviation of
10¢. How much more would we expect the shopper to spend on apples than bananas? The
standard deviation?
10. A club sells raffle tickets for $5 each. There are 10 prizes of $25 and one prize of $100. If 200
tickets are sold, and you bought one of them, what are your expected winnings? Have you paid too
much for the ticket?
11. Insurance companies compute expected values so that they can set their rates at profitable but
competitive levels. A 64 year-old man obtains a $10,000 one-year life insurance policy at a cost of
$600 per month. Based on past mortality experience, the insurance company estimates that there is a
0.963 chance that this man will live for at least one year. How much can the insurance company
expect to earn on this policy?