Exercises_ Binomial & Poisson Distribution
A. In a game called Taxation and Evasion, a player rolls a pair of dice. If on any turn the sum is 7, 11, or 12, the
player gets audited. Otherwise, she avoids taxes. Suppose a player takes 5 turns at rolling the dice.
1. The probability that she does not get audited is ________.
2. The probability that she gets audited once is ________.
3. The probability that she gets audited at least once is ________.
4. The probability that she gets audited no more than 2 times is ________.
5. The expected number of times she will be audited is ________.
6. The standard deviation of the number of times she will be audited is ________.
B. The quality control manager of Marilyn’s Cookies is inspecting a batch of chocolate chip cookies. When the
production process is in control, the average number of chocolate chip parts per cookie is 6.0.
1. What is the probability that any particular cookie being inspected has 4.0 chip parts?
2. What is the probability that any particular cookie being inspected has fewer than 5.0 chip parts?
3. What is the probability that any particular cookie being inspected has at least 6.0 chip parts
4. What is the probability that any particular cookie being inspected has between 5.0 and 8.0 inclusive chip
parts?
5. What is the probability that any particular cookie being inspected has less than 5.0 or more than 8.0 chip
parts?
C. A student is taking a multiple-choice exam in which each question has four choices. Assume that the student
has no knowledge of the correct answers to any of the questions. She has decided on a strategy in which she
will place four balls (mark A, B, C, and D) into a box. She randomly selects one ball for each question and
replaces the ball in the box. The marking on the ball will determine her answer to the question. There are five
multiple-choice questions on the exam. What is the probability that she will get
1. Five questions correct?
2. At least four questions correct?
3. No questions correct?
4. No more than two questions correct?
D. The number of 911 calls in Butte, Montana, has a Poisson distribution with a mean of 6.7 calls a day.
1. The probability of seven 911 calls in a day is ________________.
2. The probability of seven or eight 911 calls in a day is ________________.
3. The probability of 2 or more 911 calls in a day is ________________.
4. The standard deviation of the number of 911 calls in a day is ________________.
