Name ___________________________________ Period _________________
Special Topics Section 8.5 Day 2
Probability Models
1.
Suppose that each of three randomly selected customers purchasing a hot tub at a certain store chooses either an electric (E) or a gas (G) model. Assume that these customers make their choices independently of one another and that 40% of all customers select an electric model. The number among the three customers who purchase an electric hot tub is a random variable. What is the probability distribution?
2.
Let X be the number of courses for which a randomly selected student at a certain university is registered. The probability distribution appears in the accompanying table.
 What is
 What is b g
X bg
?
.
1 2 3 4 5 6 7
02 .
03 .
b g
?
09 .
25 .
40 .
16 .
05
 What is
 What is the probability that the selected student is taking at most five courses?
 What is the probability that the selected student is taking more than five courses?
 What is P 3

X

6
 What is P b g
? b

X

6 g
?
 What is the mean and standard deviation of this model?
3.
Below is a distribution for number of visits to a dentist in one year. X = # of visits to the dentist.
X 0 1 2 3 4
P X .
1 .
3 .
4 .
15 .
05
Determine the expected value and the standard deviation.
4.
Let Y denote the number of broken eggs in a randomly selected carton of one dozen “store brand” eggs at a certain market. Suppose that the probability distribution of Y is as follows:
Y 0 1 2 3 4
P Y 65 .
20 .
10 .
04
 Calculate the probability that the carton contains at most two broken eggs.
 Calculate the probability that the carton contains fewer than two broken eggs.
 Calculate the probability that the carton contains exactly ten unbroken eggs.
 Calculate the probability that the carton has at least ten eggs that are unbroken.
 Determine the expected number of broken eggs per dozen.
 Determine the variance and standard deviation.

5.
Now that the new models are here, a car dealership has lowered prices on last year’s models. An aggressive salesperson estimates the following probability distribution of X, the number of cars that she’ll sell next week.
X 0 1 2 3 4
P X 05 .
15 .
35 .
25 .
20
Determine the expected value and standard deviation.
6.
State whether each of the following random variables is discrete or continuous:
 The number of defective tires on a car.
 The body temperature of a hospital patient.
 The number of pages in a book.
 The number of draws (with replacement) from a deck of cards until a heart is selected.
 The lifetime of a light bulb.
7.
Given the following density function represents a continuous random variable Z.
1
0 2
Describe the process to calculate the two probabilities. What can we say about their probabilities?
What is
 
1

What is
 
1.5

8.
The Lewis family has 3 kids. Every Sunday, Susan, the mom, buys either 1 or 2 gallons of milk. Below is the probability distribution for the number of gallons of milk bought at the store on Sunday.
X 1 2
Find the expected value and standard deviation.
Over Christmas, grandparents come and visit. Susan will have to buy an extra gallon of milk. Complete the probability distribution for the number of gallons of milk bought.
X

1
Find the expected value and standard deviation.
Next door to the Lewis family is the Peterson family. They have 3 kids also. Unfortunately, the parents are sick, so Susan has agreed to do their shopping this Sunday. She will need to by double the amount of milk. Complete the probability distribution for the number of gallons of milk bought.
2 X
Find the expected value and standard deviation.
9.
A club sells raffle tickets for $5 each. There are 10 prizes of $25 and one price of $100. If 200 tickets are sold, determine the probability distribution. What are your expected winnings per ticket?
Have you paid too much for the ticket? Explain.

10.
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 10 lobsters is given by the following probability distribution.
X 0 1 2 3 4 5
( ) 0.48 0.28 0.17
0.05 0.01 0.01
a) How many living lobsters per crate of 10 would we expect to arrive in Japan? 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?
11.
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
( ) 0.35 0.40 0.25
Find the expected value, variance and standard deviation.