HW4, Math 320, Spring 98

Name__________________________. Due Friday, February 6.

1. This problem consists of exercises 4.38 - 4.41 on pages 156 - 157. If you know the number of games played in each of the World Series of 1992 - 1997, you are welcome to include that in the data.

1. #4.38 p. 156. Construct a probability model (that is, find the probability density function) for the number of games played and use it to find the mean for this population.
2. #4.39 p. 157. Graph the distribution function.
3. #4.40 p. 157. Find the population standard deviation.
4. #4.41 p. 157. Find the population median and interquartile range.

2. This exercise is based on #4.24 on page 146.

1. Do #4.24 on page 146.
2. What is the probability that a randomly selected tire has less than 1/8 inch of tread on it?
3. (See #4.26 on page 146). Find the distribution function and graph it.
4. Use the distribution function to find the probability that a randomly selected tire has between 1/8 and 3/8 of an inch of tread on it.
5. Find the population mean and standard deviation.

3. Mr. Smooth invites you to play a game of Chuck-a-luck. To play this game, you pick a number from 1 through 6 and then you roll three dice. If your number doesn't appear you pay Mr. Smooth one dollar. Otherwise, he will pay you one dollar for each occurrence of your number on the dice. Are you willing to play? Analyze this game as follows. Pick your number. Let X be the random variable which is your payoff on a roll of the dice: thus -1 if your number doesn't appear, otherwise the number of times your number appears.

1. List the values of X.
2. Find the probability function of X.
3. Find the expected value of X.
4. Find the standard deviation of X.
5. On average, how much do you expect to win (lose) at each roll of the dice?

4. Do #5.8 on page 177.

5. Do #5.12 on page 177. Use your calculator if it has binomial distribution functions on it. If you have a minimal calculator, like the Sharp EL546, you will have to use Excel by entering