1

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).

            266.7       136.2      1 15.0        107.0       99.4       97.8      60.0

              43.7          36.2       27.7            21.3       16.0       12.6       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.

2

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.

3

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.

4

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.