Question 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)

Isabella22.7

Sophia 20.5

Emma17.2

Olivia 16.9

Ava 15.3

Emily 14.2

Abigail14.1

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.

Question 2

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 405100

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?

Question 3

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.