GRADED PROBLEM SET #5

Answer each of the following questions completely. There are atotal of 20 points possible in the assignment.

1. (8 pts) Based on past results found in the InformationPlease Almanac there is a 0.1919 probability that a baseballWorld Series will last four games, a 0.2121 probability that itwill last five games, a 0.2223 probability that it will last sixgames, and a 0.3737 probability that it will last seven games.
   1. Does the given information describe a probability distribution?Explain.

2. Assuming that the given information describes a probabilitydistribution, find the mean and standard deviation for the numberof games in World Series.

2. (4 pts) Men heights are normally distributed with a mean of 70inches and a standard deviation of 3 inches. Doorframes have to bedesigned so that 99.9% of all men can pass under without stooping.What is the height of the doorframe?

3. (8 pts) Tree diameters in a plot of land are normallydistributed with a mean of 14 inches and a standard deviation of3.2 inches.
   1. What is the probability that an individual tree has a diameterbetween 13 inches and 16.3 inches?

2. What is the probability that an individual tree has a diameterless than 12 inches?

3. What is the probability that an individual tree has a diameterof at least 15 inches?

4. Find the cutoff for the 80^th percentile of treediameters. (Provide the probability notation)