KEY_Review for Exam 2
Ch 5, 6, 7
Chapter 5
1. Which of the following statements is not true about probability?
a. A probability of zero means that an event will not happen, a probability of one means that an event
is certain to happen.
b. Probability is used to measure how often random events occur.
c. Probabilities are always numbers between 0 and 1 inclusive.
d. All of the above are true statements
2. If 20 babies are born, how often are there 8 or less male babies? Assume that the gender of a
baby is a random event. Which of the following experiments would not simulate this situation?
a. Flip a coin twenty times. Designate a head to mean "female" and a tail to mean "male".
b. Roll a die twenty times. Designate a 1, 2, or 3 to mean "female" and a 4, 5, or 6 to mean "male".
c. Choose the first twenty digits from a row in the random number table. Designate odd numbers to
mean "female" and even numbers to mean "male".
d. All of the above will simulate the gender of twenty babies.
3. A card player declares that there is a one in thirteen chance that the next card pulled from a wellshuffled, full deck will be a queen. Is the following an example of theoretical probability or
empirical probability? Explain.
Theoretical probability because it is based on all the possible outcomes.
4. A homeowner notes that five out of seven days the newspaper arrives before 5 pm. He concludes
that the probability that the newspaper will arrive before 5 pm tomorrow is about 71%. Is the
following an example of theoretical probability or empirical probability? Explain
Empirical probability because it is based on the experiment.
5. The National Center for Health Statistics has found that there is a 0.41% chance that an American
citizen will die from falling. What is the probability that you will not die from a fall? (Round to the
nearest hundredth of a percent)
100%-0.41% = 99.59%
6. Which of the following statements is true about the Law of Large Numbers (LLN)?
a. The LLN is almost always true, but there are special occasions, even when outcomes are
random, when the LLN can be broken.
b. The LLN states that the empirical probability that is observed will simulate the
theoretical probability that is expected for any finite number of trials, so a simulation or
experiment need not have an excessive number of trials.
c. The LLN states that if you simulate or conduct an experiment or simulation enough
times the empirical probability observed will always match the theoretical probability that
is expected.
d. The LLN states that if an experiment with a random outcome is repeated a large number
of times, the empirical probability that is observed is likely to be close to the theoretical
probability
Use the following table to answer questions (7) -(12). A random sample of college students was asked to
respond to a survey about how they spend their free time on weekends. One question, summarized in the
table below, asked each respondent to choose the one activity that they are most likely to participate in on
a Saturday morning. The activity choices were homework, housework, outside employment, recreation, or
other.
Homework
29
Male
Female
Housework Outside Employment Recreation
15
20
23
18
17
47
32
26
46
Other
9
96
39
4
104
62
13
200
7. If one student is randomly chosen from the group, what is the probability that the student is
female?
104/200 = 0.52
8. If one student is randomly chosen from the group, what is the probability that the student
chose "outside employment" as their most likely activity on a Saturday morning?
46/200 = 0.23
9. If one student is randomly chosen from the group, what is the probability that the student is
female and chose "outside employment" as their most likely activity on a Saturday morning?
26/200 = 0.13
10. If one student is randomly chosen from the group, what is the probability that the student chose
"homework" or "housework" as their most likely activity on a Saturday morning?
(47+32)/200 = 0.395
11. What is the probability that a randomly chosen survey respondent is male or chose "recreation" as
their most likely activity on Saturday mornings?
(96+62-23)/200 = 135/200 =
0.675
12. Find the probability that a female college student from the group chose "housework" as their
most likely activity on Saturday mornings? (round to the nearest thousandth)
P(housework |female) = 17/104 = 0.163
13. A standard deck of card contains 52 cards. There are 26 black cards and 26 red cards. There are 4
suits: 2 red suits (diamonds & hearts) and 2 black suits (clubs and spades). Each suit contains 13
cards consisting of the following cards: 2, 3, 4, 5, 6, 7, 8, 9, 10, Jack, Queen, King, and Ace. Face
cards are considered Jack, Queen, King ONLY. Find the probability of each of the following.
a. A randomly selected card is red?
b.
P(red) = 26/52 = 1/2
A randomly selected card is a heart? P(heart) = 13/52 = 1/4
c. A randomly selected card is a heart or red? P(heart or red) = (13+26-13)/52 = 1/2
d. A randomly selected card is a face card and black? P(face and black) = 6/52 = 3/26
14. You roll a die, trying to roll a 3. You record the following die rolls: 2,3,3,6,1,5
a. Find the theoretical probability of rolling a “3”
1/6
b. Find the empirical probability of rolling a “3”.
2/6 = 1/3
Chapter 6
15. Determine whether the variable would best be modeled as continuous or discrete: The
temperature of a greenhouse at a certain time of the day.
Continuous
16. Determine whether the variable would best be modeled as continuous or discrete: The
number of tomatoes harvested each week from a greenhouse tomato plant.
Discrete
17. An MP3 playlist, containing several songs from five genres, is set to shuffle. The following
table shows the genre and the associated probability for the first song played. Does the table
represent a probability distribution? Explain.
Genre
Rock
Pop
Country
Jazz
Classica;
Probability
0.302
0.290
0.203
0.123
0.09
No because the sum of the probabilities of all genres in not equal to 1.
Use the following information for questions (18)-(20). Male players at the high school, college and
professional ranks use a regulation basketball that weighs 22.0 ounces with a standard deviation of 1.0
ounce. Assume that the weights of basketballs are approximately normally distributed.
18. Roughly what percentage of regulation basketballs weigh less than 20.7 ounces? Round to
the nearest tenth of a percent.
19. If a regulation basketball is randomly selected, what is the probability that it will weigh
between 20.5 and 23.5 ounces? Round to the nearest thousandth.
20. Some statisticians use a guideline that says that events that happen 5% of the time or less often
should be considered "unusual." By this standard, is it unusual to find a basketball that weighs
23.75 ounces or more? (Show calculations to support your answer)
Use the following information for questions (21) - (23). The average travel time to work for a person
living and working in Kokomo, Indiana is 17 minutes. Suppose the standard deviation of travel time
to work is 4.5 minutes and the distribution of travel time is approximately normally distributed.
21. Approximately what percentage of people living and working in Kokomo has a travel time to
work that is at least 20 minutes? Round to the nearest whole percent.
22. Suppose that it is reported in the news that 12 % of the people living and working in Kokomo feel
that their commute is too long. What is the travel time to work that separates the top 12% of
people with the longest travel times and the lower 88%? Round to the nearest tenth of a minute.
23. Would it be unusual to randomly select a person living and working in Kokomo whose
average travel time to work is 28 minutes? Explain.
24. The normal model N58, 21 describes the distribution of weights of chicken eggs in grams.
Suppose that the weight of a randomly selected chicken egg has a z-score of 1.78. What is the
weight of this egg in grams? Round to the nearest hundredth of a gram.
Chapter 7
25. The collection of the ages of all the U. S. first ladies when they married is a _______________.
a. Population
b. Sample
c. Parameter
d. Statistic
26. Suppose that the age of all the U. S. first ladies when they married was recorded. The mean age
of U. S. first ladies when they married would be a __________________ .
a. Population
b. Sample
c. Parameter
d. Statistic
27. Researchers are interested in learning more about the age of women when they marry for the first
time so they survey 500 married or divorced women and ask them how old they were when they
first married. The collection of the ages of the 500 women when they first married is
a_______________.
a. Population
b. Sample
c. Parameter
d. Statistic
28. Frances is interested in whether students at his college would like to see a portion of the campus
preserved as green space. Using student numbers, he randomly contacts 300 students and
receives a response from 75. Of those who responded, 64% favored the preservation of green
space on campus. This scenario is describing what type of sampling bias?
a. Measurement bias
b. Survey bias
c. Voluntary response bias
d. Nonresponse bias
29. Max organizes weekly concerts in the local park. He is interested in knowing what type of
music people enjoy. Before one particular concert, he makes an announcement to the audience,
and asks people to visit a web page and take a survey to vote on whether or not they liked the
concert. 75 people take the survey, and 58% respond favorably. Max claims that 58% of all of
those who were at the concert liked the music. What type of bias is in Max's method?
a. Measurement bias
b. Survey bias
c. Voluntary response bias
d. Nonresponse bias
30. Which of the following statements is true about the confidence interval for a population
proportion?
a. It is equal to the population proportion plus or minus a calculated amount called the
standard error.
b. It is equal to the sample proportion plus or minus a calculated amount called the margin of
error.
c. The confidence interval for a proportion will always contain the true population
proportion.
d. The confidence interval for a proportion does not need a specified confidence level.
31. Complete the statement by filling in the blank. When constructing a confidence interval, if the
level of confidence increases the margin of error will _________________ and the confidence
interval will be _________________. A larger sample size will improve the accuracy of the
confidence interval, therefore margin of error will _________________ and the confidence
interval will be _________________.
a. Decrease, narrower. Increase, wider.
b. Decrease, wider. Increase, narrower
c. Increase; narrower. Decrease, wider.
d. Increase; wider. Decrease; narrower.
Use the following information to answer questions (32)-(35). In a recent poll of 1200 randomly selected
adult office workers, 32% said they had worn a Halloween costume to the office at least once.
32. What is the standard error for the estimate of the proportion of all American adult office workers
that have worn a Halloween costume to the office? Round to the nearest ten-thousandth.
33. What is the margin of error, using a 95% confidence level, for estimating the true population
proportion of adult office workers who have worn a Halloween costume to the office at least
once? (Round to the nearest thousandth)
34. Report the 95% confidence interval for the proportion of all adult office workers who have
worn a Halloween costume to the office at least once
35. Draw the confidence interval support claim based on the confidence interval from the
previous problem.
We are 95% confident that the true population proportion of all office workers who had worn a
Halloween costume is between 29.4% and 34.6%.
36. A random sample of 830 adult television viewers showed that 52% planned to watch sporting
event X. The margin of error is 3 percentage points with a 95% confidence. Does the confidence
interval support the claim that the majority of adult television viewers plan to watch sporting
event X? Why?
95%CI: (0.52-0.03, 0.52+0.03) = (0.49, 0.55) = (49%, 55%)
No, the confidence interval means that we are 95% confident that the population proportion of
adults television viewers who plan to watch sporting event X is between 49% and 55%. The true
population proportion could be less than 50%.
37. Suppose that in a recent poll of 1200 adults between the ages of 35 and 45, 38% surveyed said
they have thought about getting elective plastic surgery. Find the 95% confidence interval for the
proportion of adults ages 35 to 45 who have thought about getting elective plastic surgery then
choose the correct interpretation. (Round to the nearest tenth of a percent). Draw the confidence
interval support claim.
We are 95% confident that the true population proportion of adults between ages of 35 to 45 who
thought about getting elective plastic surgery is between 35.2% and 40.8%.
38. A polling agency wants to determine the size of a random sample needed to estimate the
proportion of homeowners who keep a hand gun in their home for security. The estimate
should have margin of error no more than 2.5 percentage points at a 95% level of confidence.
Determine the minimum size of the sample, rounding to the nearest whole person.