Download Homework 2

Probability Distribution Homework 2
Chapters 7 & 8
1. John Smith sells new cars for Johnson Ford. John usually sells the largest number
of cars on Saturday. He has the following probability distribution for the number
of cars he expects to sell on a particular Saturday.
# of Cars Sold (X)
0
1
2
3
4
P(X)
.10
.20
.30
.30
.10
a.
b.
c.
d.
What type of distribution is this? (discrete or continuous probability distribution)
On a typical Saturday, how many cars does John expect to sell?
What is the variance and standard deviation? OMIT
If another salesperson, Rita Jones, had the same mean sales, but a standard
deviation of 1.91 cars, which salesperson would you consider more consistent
(Rita or John)? OMIT
e. How would you interpret the standard deviation for John’s Saturday sales. OMIT
2.
During a study of the complaints logged in against the employees of First Savings
and Loan has ranged from 0 to 6 each day for the past month when they have
been opened. Calculate the expected value and standard deviation (OMIT std.
dev.). Interpret each.
Complaints
0
1
2
3
4
5
6
Total
Number of Days
3
4
3
6
2
1
4
23
Page 1 of 3
3.
General Mills packages Cheerios in 36-ounce boxes that have a standard
deviation of 1.9 ounces. Assume a normal distribution for the weights. If you
select one box at random, what is the probability the box will weigh:
a. Less than 34.8 ounces?
b. More than 34.8 ounces?
c. Between 34.4 ounces and 38.9 ounces?
d. Between 39.5 ounces and 41.1 ounces?
4.
Wages at a General Motors assembly plant average $22.87 per hour, with a
standard deviation of $5.87. What must your hourly wage be if you want to earn .
..
a. More than 80% of all employees?
b. More than 30% of all employees?
c. More than 50% of all employees?
d. In the interquartile range?
5.
Monthly production costs for a print shop have averaged $410 with a standard
deviation of $87. The manager commits to the owner that he will hold costs
below $300 per month. If costs are normally distributed, can the owner believe
the manager?
6.
Students taking the Graduate Management Aptitude Test averaged 812 with a
standard deviation of 145. Only those in the top 20 percent can apply for a
particular scholarship. You have scored 900 on the test. Should you apply?
7. The broadcast networks introduce new television shows each fall. In an attempt
to get viewers interested in the new shows, television commercials are aired
during the summer as part of a promotional campaign conducted prior to the fall
debuts. The networks then conduct surveys to see what percentage of the viewing
public is aware of the shows. According to network sources, in the fall of 2001,
45% of viewers were aware of the new series Criminal Intent. Given that a
random sample of 20 viewers selected, what is the probability that:
a. Fewer than 5 viewers are aware of Criminal Intent?
b. 10 or more viewers are aware of Criminal Intent?
c. 15 or more viewers are aware of Criminal Intent?
d. 5 or more viewers are aware of Criminal Intent?
e. All 20 are aware of Criminal Intent?
f. What is the expected number of viewers in the sample of 20 that will be
aware of Criminal Intent?
Page 2 of 3
8. The commission rate commercial airlines pay travel agents has been declining for
several years. In an attempt by travel agencies to raise revenue, many agencies
are now charging their customers a ticket fee, typically between $10 and $15.
According to the American Society of Ticket Agents, about 90% of travel agents
charge customers fees when purchasing an airline ticket. Compute the probability
that of 10 randomly selected travel agencies:
a. zero charges ticket fees?
b. Exactly six charge ticket fees?
c. 7 or more charge ticket fees?
d. Less than 7 charge ticket fees?
For more binomial distribution practice consider the problems in Chapter 7 pages 221223. 7-90, 7-92, 7-100.
Page 3 of 3