Business Statistics
cameron529
homework_23.docx1. The U.S. Bureau of Justice released the following probabilities for those arrested for committing various felony crimes in the United States
|
Probability of Being |
|||
|
Crime |
Prosecuted |
Convicted |
Jailed for >1 Year |
|
Homicide Assault Burglary Arson Drug Offenses Weapons Public Disorders |
0.91 0.79 0.88 0.88 0.78 0.83 0.92 |
0.75 0.64 0.81 0.72 0.69 0.70 0.85 |
0.73 0.15 0.28 0.28 0.19 0.13 0.12 |
David has been arrested for Homicide, Bill has been arrested for a weapon offense, and Dan has been arrested on burglary. Assuming these individuals are typical perpetrators and the decisions regarding their respective fates are unrelated, determine the probability that: (10 points)
(A) David will be jailed for more than a year
(B) Either David or Bill will be convicted
(C) None of the three will be jailed for more than a year
(D) David and Bill will be convicted, but Dan will be found innocent
(E) None will be prosecuted
2. A construction company has bid on two contracts. The probability of winning contract A is 0.3. If the company wins contract A, then the probability of winning contract B is 0.4. If the company loses contract A, then the probability of winning contract B deceases to 0.2. Find the probability of the following events (10 points)
(A) Construct a tree diagram for this problem
(B) Compute the probability of winning both contacts, that is,
(C) Compute the probability of winning exactly one contract, that is,
(D) Winning at least one contract, that is,
3. According to the National Marine Manufacturers Association, 50% of the population of Vermont were boating participants during the most recent year. For a randomly selected sample of 20 Vermont residents, with the discrete random variable x=the number in the sample who were boating participants that year, calculate the following. (10 points)
(You can construct an excel table as shown on page 180, to compute probabilities)
(A) E(x)
(B)
(C)
4. The U.S. divorce rate has been reported as 3.6 divorces per 1000 population. Assuming that this rate applies to a small community of just 500 people and is Poisson distributed and that x=the number of divorces in this community during the coming year, determine the following, (10 points)
(You can construct an excel table as shown on page 191, to compute probabilities)
(A) E(x)
(B)
(C)
