Question

Part 1

Armadillos are among the most common of Florida’s roadkill victims. A study done along the Ronald Reagan Turnpike in central Florida found an average of 1.9 armadillo roadkills per 100 miles during the winter, when armadillos are least active [Source: M. Inbar and R. T. Mayer, “Spatio-temporal trends in armadillo diurnal activity and road-kills in central Florida,” Wildlife Society Bulletin 27, no. 3 (1999).]

It’s New Year’s Day, and you and your friends are on a road trip in Florida. You drive 100 miles on the Ronald Reagan Turnpike. The probability that you see exactly three armadillo roadkills is:   

• 0.1253
• 0.2158
• 0.0646
• 0.1710

The probability that you see more than six armadillo roadkills while motoring 100 miles on the Ronald Reagan Turnpike on New Year’s Day is:

• 0.0034
• 0.0653
• 0.0098
• 0.0132

.The next day, you drive 200 miles on the Ronald Reagan Turnpike. The probability that you observe no more than eight armadillo roadkills this day on the highway is:

• 0.8766
• 0.9840
• 0.5265
• 0.0160

The number of roadkill sightings over 250 miles has an expected value of:   

• 1.9
• 8.75
• 10
• 4.75

and a standard deviation of:

• 3.16
• 2.18
• 2.96
• 4.75

Part 2

In the New York Lotto, there are 51 balls numbered 1 to 51 in a barrel. To enter the lottery, you select six numbers. Then six balls are randomly drawn from the barrel without replacement to determine the six winning numbers.

The probability that you match exactly three of the winning numbers is:

• 0.0158
• 0.1241
• 0.0008
• 0.0224

To win the jackpot, you must match all six winning numbers. However, most lotteries award small prizes for matching a subset of the winning numbers.

Suppose that you are awarded prize money if you match at least three of the winning numbers. The probability that you will win some prize money is:

• 0.0291
• 0.0008
• 0.0166
• 0.0210

Let x be the number of matches between your six numbers and the winning six numbers. How many different values can the random variable x take on?

7

6

An infinite number of values

36

42

The expected value of the random variable x is:

• 0.7660
• 0.7059
• 0.8571
• 0.8000

The standard deviation of the distribution is:

• 0.5606
• 0.7487
• 0.8032
• 0.7839

Suppose that the New York Lotto only awards a jackpot prize: you must match all six winning numbers to win prize money. You will see that f(6) displays as <0.0001 on the distribution graph to indicate that its value is smaller than the smallest number that can be displayed (0.0001) and larger than 0. The value of f(6) carried out to 12 decimal places is:

f(6) = 0.000000055526

Assume that if you match all six winning numbers, no one else matches (to avoid the complication of splitting the jackpot).

The jackpot this week is $10 million, and it costs $4 to enter the lottery. Terese, a statistics student, is trying to decide whether or not to buy one ticket. She defines a random variable x that can take on two values, $0 or $10 million, and she bases her decision on its expected value. She will decide to buy a ticket if the expected value of x exceeds the cost of the ticket.

Terese will decide_____ a lottery ticket this week.  

• to buy
• not to buy

Answer 1

Part 1