Exam 5: Discrete Probability Distributions

Carlson Jewelers permits the return of their diamond wedding rings, provided the return occurs within two weeks of the purchase date. Their records reveal that 10 percent of the diamond wedding rings are returned. Five different customers buy five rings. What is the probability that none will be returned?

David's gasoline station offers 4 cents off per litre if the customer pays in cash and does not use a credit card. Past evidence indicates that 40% of all customers pay in cash. During a one-hour period twenty-five customers buy gasoline at this station. What is the probability that at least ten pay in cash?

A statistic professor finds she averages five e-mail messages per day from students. Assume the number of messages approximates a Poisson distribution. What is the probability that on a randomly selected day she will have two messages?

The marketing department of a nationally known cereal maker plans to conduct a national survey to find out whether or not consumers of flake cereals can distinguish one of their favourite flake cereals. To test the questionnaire and procedure to be used, eight persons were asked to cooperate in an experiment. Five very small bowls of flake cereals were placed in front of a person. The bowls were labeled A, B, C, D, and

A hybrid-grower is experiencing trouble with corn borers. A random check of 5,000 ears revealed the following: many of the ears contained no borers. Some ears had one borer; a few had two borers; and so on. The distribution of the number of borers per ear approximated the Poisson distribution. The grower counted 3,500 borers in the 5,000 ears. What is the probability that an ear of corn selected at random will contain no borers?

Elly's hot dog emporium is famous for its chilidogs. Some customers order the hot dogs with hot peppers, while many do not care for that added bit of zest. Elly's latest sales indicate that 30% of the customers ordering her chili dogs order it with hot peppers. Suppose 18 customers are selected at random. This situation is an example of what type of distribution?

A true-false test consists of five questions. If you guess the answer to each question, what is the probability of getting all five questions correct?

i. A binomial distribution is a discrete probability distribution. ii. To construct a binomial distribution, it is necessary to know the total number of trials and the probability of success on each trial. iii. If the probability of success remains the same, but n increases, the shape of the binomial distribution becomes more symmetrical.

In which of the following discrete distribution does the probability of a success vary from one trial to the next?

If the variance of a probability was computed to be 3.6 grams, what is the standard deviation?

Elly's hot dog emporium is famous for its chilidogs. Some customers order the hot dogs with hot peppers, while many do not care for that added bit of zest. Elly's latest sales indicate that 30% of the customers ordering her chili dogs order it with hot peppers. Suppose 18 customers are selected at random. What is the probability that fifteen or more customers will want hot peppers?

A company is studying the number of monthly absences among its 125 employees. The following probability distribution shows the likelihood that people were absent 0, 1, 2, 3, 4, or 5 days last month. What is the mean number of days absent?

i. A random variable is assigned numerical values based on the outcomes of an experiment. ii. A random variable is a quantity resulting from a random experiment that can assume different values by chance. iii. The mean of a probability distribution is referred to as its expected value.

The information below is the number of daily emergency assists made to skiers by the volunteer ski team at Alpine Ski Lodge for the last 50 days. To explain, there were 22 days on which there were 2 emergency assists, and 10 days on which there were 3 emergency assists. Convert this information to a probability distribution, and determine the mean number of assists per day.

(i. A probability distribution relates the expected outcomes of an experiment to the probability of each one occurring. (ii) The probability of all events in a probability distribution must sum to one. (iii) A finite population consists of a fixed number of individuals, objects, or measurements.

The probabilities and the number of automobiles lined up at a Lakeside Olds at opening time (7:30 a.m.) for service are: On a typical day, what is the standard deviation of the number of cars that Lakeside Olds can expect to be lined up at opening?

If n = 100 and p= 1/5, determine the mean and standard deviation of this binomial distribution.

The information below is the number of daily emergency assists made to skiers by the volunteer ski team at Alpine Ski Lodge for the last 50 days. To explain, there were 22 days on which there were 2 emergency assists, and 9 days on which there were 3 emergency assists. Convert this information to a probability distribution, and determine the mean number of assists per day.

Which of the following is a requirement for use of the hypergeometric distribution?

The arrival of customers at a service desk follows a Poisson distribution. If they arrive at the rate of two every five minutes, what is the probability that no customers arrive in a five-minute period?