There is a game at the carnival that costs $20 to play. There are two outcomes: either you win $100, or you lose. To play, you roll a die. If a six appears, you win; all other rolls, you lose.

1.What is the mean (or the expected value) of the game?

Answer Choices:

-$1.66

-$3.33

$1.66

$3.33

2.If 1000 people played this game during one afternoon, what would you expect to be the outcome?

Answer Choices:

The game earns $3330.

The game earns $1660.

The game loses $3330.

The game loses $1660.

For questions 6 - 7, use the described binomial probability distribution to calculate the mean (expected value) and the standard deviation.

Brent golfs for the Forestville Knights High School team. When he practices his putting, he can make a 10-foot putt 80% of the time.

6.If Brent takes 200 putts for practice, what is the average number of putts he will make?

Answer Choices:

120

140

160

180

7.If Brent takes 200 putts for practice, what is the standard deviation of the number of putts he will make?

Answer Choices:

5.66

11.31

16

32

For questions 8 - 12, use the described situation to calculate the probabilities requested.

The ski lift at Thunder Mountain called Devils Canyon is quite dangerous. Usually 2% of the skiers who attempt the run will injure themselves due to falls.

8.What is the probability that exactly 3 of the next 100 skiers who attempt this run will injure themselves?

Answer Choices:

0.126

0.175

0.182

0.215

9.What is the probability that no more than 5 of the next 100 skiers who attempt this run will injure themselves?

Answer Choices:

0.1867

0.7652

0.8899

0.9845

10.What is the probability that more than 3 of the next 100 skiers who attempt this run will injure themselves?

Answer Choices:

0.141

0.182

0.221

0.297

11.What is the probability that the first skier to be injured will not occur until the 20th skier?

Answer Choices:

0.0005

0.0101

0.0136

0.0272

12.What is the probability that the first skier to be injured will occur within the first 10 skiers?

Answer Choices:

0.156

0.183

0.298

0.364

For questions 13 - 17, use the described situation to calculate the probabilities requested.

Henry had a batting average of 0.341 last season (out of 1000 at-bats, he had 341 hits). Given that this batting average will stay the same this year, answer the following questions.

13.What is the probability that his first hit will not occur until his 5th at-bat?

Answer Choices:

0.064

0.083

0.129

0.166

14.What is the probability that his first hit will occur within his first 5 at-bats?

Answer Choices:

0.654

0.765

0.821

0.876

15.Of his next 20 at-bats, what is the probability that he gets exactly 8 hits?

Answer Choices:

0.114

0.129

0.154

0.297

16.Of his next 20 at-bats, what is the probability that he gets at least 8 hits?

Answer Choices:

0.285

0.366

0.547

0.634

17.Of his next 20 at-bats, what is the probability that he gets no more than 8 hits?

Answer Choices:

0.622

0.645

0.729

0.788

For questions 18 - 20, use the given mean and standard deviation to answer the following questions.

The average GPA at the University of North Carolina is a 3.2 with a standard deviation of 0.3. Assume that all GPA's at the University of North Carolina are normally distributed when answering the following questions.

18.What is the probability of randomly selecting a student at the University of North Carolina with a GPA of 2.9 or lower?

Answer Choices:

0.10

0.16

0.24

0.31

19.What is the probability of randomly selecting a student at the University of North Carolina with a GPA between 2.9 and 3.5?

Answer Choices:

0.34

0.68

0.75

0.95

20.What is the probability of randomly selecting a student at the University of North Carolina with a GPA higher than 3.7?

Answer Choices:

0.023

0.048

0.058

0.977