) Jane Watson is running a youth recreation program to reduce the juvenile crime rate. If Jane can get a Law Enforcement Assistance Administration (LEAA) grant to expand the program, she feels that there is a .9 probability that the program will work. If she fails to get the grant, the probability of success falls to .3. If the probability of getting the LEAA grant is .6, what is the probability that Jane’s program will be successful?
2) Given P(A)=.21, P(B|A)=.75, and P(A|B)=.41, Calculate:
a)P(A ꓵ B)
(b) P(B)
3) Sheriff Joe Bob Stewart thinks the odds of any law enforcement grant being funded are .25. He believes that the decision to fund one grant is independent of the decision to fund any other grant. (a) Use a probability tree to tell Sheriff Stewart what the probability is that he can submit three grants and get none funded.
(b) What is the probability of getting exactly one funded?
(c) Exactly two?
(d) Two or more
4)In your own words, explain what mutually exclusive events are.
5)In a group of 40 people, 10 are healthy and every person of the remaining 30 has high blood pressure, a high level of cholesterol or both. If 15 have high blood pressure and 25 have high level of cholesterol, how many people have high blood pressure and a high level of cholesterol?
If a person is selected randomly from this group, what is the probability that he/she
6)Explain the two general rules of probability?
7)Th e director of development at the Midfield Wisconsin Museum of the Arts has recently collected data on donations for the past several years. She finds that the data are normally distributed with a mean of $23 and a standard deviation of $3.57. Th e director’s ideal point for a minimum donation is $25. What percentage of individual donations are $25 or more? What percentage of individual donations are less than $25? Th e director’s long-term goal for an average individual donation is at least $40. Based on the current data, does achieving this goal seem reasonable in the immediate future?
8) Administrators at the national headquarters of the Center for the Display of Visual Arts are authorized to make small work-related purchases using purchasing cards. Th e average amount administrators charge to their cards per month is $278 with a standard deviation of 33 dollars. Th e data are normally distributed. Th e auditing staff at the center is concerned with the spending patterns of an administrator who has averaged $349 per month in charges. What percentage of balances are between $278 and $349 per month? What percentage of balances exceed $349 per month? Should the auditing staff be concerned about the spending habits of this particular administrator?
