1. What are the requirements for each distribution?

Binomial:

Geometric:

  1. Match the following:

Symbols / Description
_____ n / a. The probability of success
_____ p / b. The number of successful trials
_____ q / c. The number of trials
_____ x / d. The probability of failure
  1. What are the two properties of a probability distribution?
  1. Find the mean and standard deviation of the following probability distribution representing the number of busy phone lines.

x / P(x)
0 / 0.052
1 / 0.154
2 / 0.232
3 / 0.24
4 / 0.174
5 / 0.105
6 / 0.043
  1. Student Council is sponsoring a spring break Caribbean cruise raffle. The proceeds will to be donated to the local veterans. A local travel agency donated the cruise, valued at $2,000. The students sold 2852 raffle tickets at $5 per ticket. Kevin bought six tickets, what are Kevin’s expected earnings?
  1. A ski resort loses $70,000 per season when it does not snow very much and makes $250,000 profit when it does snow a lot. There is a 0.40 probability of it snowing at least 75 inches (a good season) this year. What is the ski resort’s expected profit this season?

For 7 and 8, determine whether the experiment is a binomial experiment. Explain. If it is, list the values of n, p, q, and x.

  1. Fifty-seven percent of families say that their children have an influence on their vacation destinations. Consider a random sample of six families who are asked whether their children have an influence on their vacation destination.
  1. Bags of plain M&M’s contain 30% brown candies. Seven pieces of candy are selected from a bag and are not replaced. The random variable represents the number of brown candies selected.
  1. Determine which of the following represents a discrete random variable. Check the ones that apply.

____ The number of cars ticketed in a the student parking lot each day

____ The amount of gasoline in gallons it takes to fill your car’s gas tank

____ The number of intercom interruptions during period 8 each week

____ The number of shoes Ms. Halliday owns

____ The number of inches a student grows during his or her junior year

  1. A study conducted at Seneca Valley Senior High School shows that 70% of graduating seniors continue their education by attending a university, community college, or associate degree program. Find the probability that among 12 randomly selected seniors at Seneca…
  1. at least 6 will continue their education beyond high school.
  1. at most 4 continue their education beyond high school.
  1. Calculate the mean and standard deviation of the distribution.
  1. A proficiency test includes a true-and-false question. Suppose that the 12 test subjects randomly guess their responses.
  1. What is the probability that exactly 5 answer the question correctly?
  1. What is the probability that at most 5 subjects answer the question correctly?
  1. What is the probability more than 5 subjects answer the question correctly?
  1. Find the mean and standard deviation of the number with correct responses.
  1. Jason is rolling a die. What is the probability of rolling a 1
  1. on the 5th roll?
  1. no more than 7 rolls?
  1. at least on the 3rd roll?
  1. A recent study of robberies for Butler County showed an average of one robbery per 5,000 people. In a town of 15,000 people find the probability
  1. of exactly 4 robberies
  1. at most 2 robberies
  1. at least 4 robberies
  1. A top NHL hockey player makes 93% of his shots in a shooting competition.
  2. What is the probability that the player will not miss the goal until his 20th try?
  1. What is the probability that the player will make seven of ten shots?
  1. What is the probability that the player will make at least 8 shots out of 10?
  1. What is the probability that the player will miss at least 8 shots out of ten?
  1. What is the probability that the player will make at most 9 shots out of ten?