1

The following table gives the seven most common first names among girls born in the United States during 2010 along with their frequencies (in thousands).

Name Number of girls

(in thousands)

Isabella 22.7

Sophia 20.5

Emma 17.2

Olivia 16.9

Ava 15.3

Emily 14.2

Abigail 14.1

Source: U.S. Social Security Administration, uww.ssa.gov.

Draw two bar graphs for these data, the first without truncating the frequency axis, and the second by truneating this axis. In the second graph, mark the number of girls on the vertical axis starting with 13.0. Briefly comment on the two bar graphs.

2

According to the Kaiser Family Foundation, U.S. workers who had employer-provided health insurance paid an average premium of $4129 for family coverage during 2011 (USA TODAY, October 10, 2011). Suppose that the premiums for such family coverage paid this year by all such workers have a bell-shaped distribution with a mean of $4129 and a standard deviation of $600. Using the empirical rule, find the approximate percentage of such workers who pay premiums for such family coverage between

a. $2329 and $5929b. $3529 and $4729c. 32929 and $5329

3

The following data give the 2009 estimates of crude oil reserves (in billions of barrels) of Saudi Arabia, Iran, Iraq, Kuwait, Venezuela, the United Arab Emirates, Russia, Libya, Nigeria, Canada, the United States, China, Brazil, and Mexico (source: www.eia.gov).

266.7136.21 15.0107.099.497.860.0

43.736.227.721.316.012.6 10.5

Prepare a box-and-whisker plot. Is the distribution of these data symmetric or skewed? Are there any outliers? If so, classify them as mild or extreme.

4

The television game show The Price Is Right has a game called the Shell Game. The game has four shells, and one of these four shells has a ball under it. The contestant chooses one shell. If this shell contains the ball, the contestant wins. If a contestant chooses one shell randomly, what is the probability of each of the following outcomes?

a. contestant winsb. contestant loses

Do these probabilities add up to 1.0? If yes, why?

5

Two thousand randomly selected adults were asked if they are in favor of or against cloning. The following table gives the responses.

In Favor Against No Opinion

Male 395 405 100

Female 300 680 120

a.If one person is selected at random from these 2000 adults, find the probability that this person is

i. in favor of cloning

ii. against cloning

iii. in favor of cloning given the person is a female

iv. a male given the person has no opinion

b.Are the events "male" and ' 'in favor" mutually exclusive? What about the events "in favor" and "against?" Why or why not?

c.Are the events "female" and "no opinion" independent? Why or why not?

6

There are a total of 160 practicing physicians in a city. Of them, 75 are female and 25 are pediatricians. Of the 75 females, 20 are pediatricians. Are the events "female" and "pediatrician" independent? Are they mutually exclusive? Explain why or why not.

7

In a political science class of 35 students, 21 favor abolishing the electoral college and thus electing the President of the United States by popular vote. If two students are selected at random from this class, what is the probability that both of them favor abolition of the electoral college? Draw a tree diagram for this problem.

8

According to the Recording Industry Association of America, only 37% of music files downloaded from Web sites in 2009 were paid for. Suppose that this percentage holds true for such files downloaded this year. Three downloaded music files are selected at random. What is the probability that all three were paid for? What is the probability that none were paid for? Assume independence of events.

9

The following table gives a two-way classification of all basketball players at a state university who began their college careers between 2004 and 2008, based on gender and whether or not they graduated.

Graduated Did Not Graduate

Male 126 55

Female 133 32

If one of these players is selected at random, find the following probabilities.

a.P(female or did not graduate)

b.P(graduated or male)

10

A contractor has submitted bids on three state jobs: an office building, a theater, and a parking garage. State rules do not allow a contractor to be offered more than one of these jobs. If this contractor is awarded any of these jobs, the profits earned from these contracts are $10 million from the office building, $5 million from the theater, and $2 million from the parking garage. His profit is zero if he gets no contract. The contractor estimates that the probabilities of getting the office building contract, the theater contract, the parking garage contract, or nothing are .15, .30, .45, and . 10, respectively. Let x be the random variable that represents the contractor's profits in millions of dollars. Write the probability distribution of x. Find the mean and standard deviation of x. Give a brief interpretation of the values of the mean and standard deviation.

Draw graphs in excel.