Wetzel                                                                                                             

Math 120

Test #3

 1.)  The following probability distribution is based on past results of Baseball World Series found in the Information Please Almanac.  The World Series is a series of games where the first team to win four out of a maximum of seven games wins the championship.  The random variable x represents the number of games played in the series.

            a.)  Find the expected number of games played in the World Series.

            b.)  Find the probability of the World Series lasting at least 6 games.

2.)  Find the following probabilities.

            a.)  P(z < 3.02)                                     b.)  P(.42 < z < 3.80)

3.)  Find the z-score that corresponds with the 28^th percentile, .

4.)  Replacement times for TV sets are normally distributed with a mean of 8.2 years and a standard deviation of 1.1 years. 

            a.)  Find the probability that a randomly selected TV will have a replacement time less than 5 years.

            b.)  Find the probability that a randomly selected TV will have a replacement time between 8 and 10 years.

            c.)  If 40 TVs are randomly selected, find the probability that their sample mean is less than 8 years.

5.)  Cans of Coca-Cola are filled so that the actual amount have a mean of 12.0 oz and a standard deviation of 0.11 oz.  Find the probability that sample of 36 cans will have a mean amount of at least 12.19 oz.

6.)  The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days.

            a.)  Find the probability of a pregnancy lasting less than 230 days.

            b.)  What is the minimum number of days you must be pregnant to be in the top15%?

7.)  A mandatory competency test of high school sophomores has a normal distribution with a mean of 400 and a standard deviation of 100.  If the bottom 7% must go to summer school, what is the minimum score you would need so to stay out of this group?

8.)  In a survey, 63% of Americans said they own a pet.  If 14 Americans are randomly selected, find the following probabilities:    

            a.)  that exactly 6 people own pets.

            b.)  that at most 9 people own pets.