MATH&146

Exam 1 Review

Lessons 1 – 11

1

Example 1

If you flip a fair coin and get heads 10 times in a

row, what is the chance of getting tails on the next

flip?

2

Example 2

Shelly is going to flip a coin 50 times and record

the percentage of heads she gets. Her friend

Diane is going to flip a coin 10 times and record

the percentage of heads she gets. Which person

is more likely to get 20% or fewer heads? Why?

Answer: For Shelly, the probability of 20% or

fewer is 0.0000119. For Diane, the probability is

0.0547. Diane is more than 4500 times more likely

than Shelley to get 20% or fewer heads!

3

Example 3

Box A and Box B are filled with red and blue

marbles as follows. Each box is shaken.

a) You want to get a blue marble, but you are only

allowed to pick out one marble without looking.

Which box should you choose, or does it

matter? Explain your answer.

4

Example 3 continued

b) Now suppose you want to pick two blue

marbles with two picks. Which box should you

choose now, or does it matter? Explain your

answer.

5

Example 4

Which is the more likely event: (a) Rolling two fair,

six-sided dice and having the sum of those dice be

ten, or (b) Flipping a fair coin four times and

getting all heads?

6

Example 5

A 2010 SurveyUSA poll asked 500 Los Angeles

residents, "What is the best hamburger place in

Southern California?" The distribution of responses by

gender is shown below.

7

Male Female Total

Five Guys Burgers 5 6 11

In-N-Out Burger 162 181 343

Fat Burger 10 12 22

Tommy's Hamburgers 27 27 54

Umani Burger 5 1 6

Other 26 20 46

Not Sure 13 5 18

Total 248 252 500

Example 5 continued

a) What is the probability that a randomly chosen

male likes Fat Burger the best?

b) What is the probability that a randomly chosen person

likes In-N-Out best or that person is female?

8

Male Female Total

Five Guys Burgers 5 6 11

In-N-Out Burger 162 181 343

Fat Burger 10 12 22

Tommy's Hamburgers 27 27 54

Umani Burger 5 1 6

Other 26 20 46

Not Sure 13 5 18

Total 248 252 500

Example 5 continued

c) What is the probability that a randomly chosen person

likes Tommy's Hamburgers and that person is male?

9

Male Female Total

Five Guys Burgers 5 6 11

In-N-Out Burger 162 181 343

Fat Burger 10 12 22

Tommy's Hamburgers 27 27 54

Umani Burger 5 1 6

Other 26 20 46

Not Sure 13 5 18

Total 248 252 500

Example 6

Of all adults in the United States, 40% have an

allergy. A random selection of 1200 adults resulted

in 32.6% reporting an allergy.

a) What is the population?

b) What is the sample?

c) Identify the statistic and give its value.

d) Identify the parameter and give its estimated

value.

10

Example 7

Determine the correct variable type: regular

categorical, ordinal, discrete, or continuous.

a) Age of a pet (in years)

b) Favorite television show

c) Number of books in a library

d) Level of education (less than high school, high

school, college, graduate school)

11

Example 8

Does regular exercise reduce the risk of a heart

attack? Here are 2 ways to study the question.

Study 1: A researcher finds 2000 men who are over

40 who exercise regularly and have not had a heart

attack. She matches each with a similar man who

does not exercise regularly, and follows both groups

for 5 years to see what % had a heart attack.

continued

12

Example 8 continued

Study 2: A researcher finds 4000 men aged over 40

who have not had heart attacks and are willing to

participate. She randomly assigns 2000 of them to a

regular program of supervised exercise. The other

2000 continue with their usual habits. She follows

them for 5 years to see what % had a heart attack.

Which study is the experiment: Study 1 or Study 2?

Using the criterion for a well-designed experiment,

critique the one that you have determined to be the

experiment. Is it well designed? Why or why not?

13

Example 9

Four students at a local high school conducted surveys.

• Shannon got the names of all 800 children in the high school and put them in a hat, and then pulled out 60 of them.

• Jake asked 10 students at an after-school meeting of the computer games club.

• Adam asked all of the 200 children in Grade 10.

continued

14

Example 9 continued

• Claire set up a booth outside of the school. Anyone

who wanted to stop and fill out a survey could. She

stopped collecting surveys when she got 60

students to complete them.

Who do you think has the best sampling method?

Why?

15

Example 10

A test to measure aggressive tendencies was given to

a group of teenage boys. The test is scored from 10 to

60, with higher scores indicating more aggression.

The histogram represents the results for these 28

boys. Which statistic is larger, the mean or the

median?

16

Example 11

Calculate the mean, median, and standard deviation

for the following data, and compute the z-score for a

value of 7. (Round to two decimal places, if

necessary.)

17

Value Frequency

0 8

1 4

2 9

3 12

4 2

5 8

6 2

8 5

Example 12

Determine which graph has the higher standard

deviation (it is not necessary to do any calculations

to answer this question). Explain your reasoning.

18

Example 13

The following box plot shows the U.S. population

for 1990.

a) Are there fewer or more children (age 17 and

under) than senior citizens (age 65 and over)?

b) 12.6% are age 65 and over. Approximately

what percent of the population are of working

age adults (above age 17 to age 65)?19

Example 14

Here are boxplots of the 2008 payrolls of all NFL and

MLB teams. (Payrolls are in millions of dollars.)

Describe what these boxplots tell you about the

payrolls for each sport and how the two payrolls are

different. (Note: the boxplots are of all the team

payrolls, not individual players.)20

Example 15

Suppose that college students are asked to identify

their preferences in political affiliation and in ice cream.

Their responses are presented below.

What proportion of respondents from each party prefer

chocolate ice cream. Are political affiliation and

favorite ice cream independent?

21

Chocolate Vanilla Strawberry Total

Democrat 13

Republican 45 8 65

Independent 9 13 4

Total 68 25 173