Exam 5: Discrete Probability Distributions

The distribution for the number of emergency calls to a city's 911 emergency number in a one-hour time period is likely to be described by a binomial distribution.

The Colbert Real Estate Agency has determined the number of home showings given by its agents is the same each day of the week.Then the variable,number of showings,is a continuous distribution.

The following probability distribution has been assessed for the number of accidents that occur in a Midwestern city each day: The probability of having less than 2 accidents on a given day is:

A warehouse contains 5 parts made by the Stafford Company and 8 parts made by the Wilson Company.If an employee selects 3 of the parts from the warehouse at random,the probability that none of the 3 parts is from the Wilson Company is approximately .03496.

The manager of a fast food store realizes that his staffing problems are a result of the variation in the number of customers that arrive at the store.If the same number of customers came each hour,she would know exactly how many servers to have working.It turns out that the Poisson distribution works well to describe the arrivals of customers in any given hour.Explain why the manager has more trouble staffing the store during those hours when the average arrival rate is higher.

Assuming that potholes occur randomly along roads,the number of potholes per mile of road could best be described by the:

Which of the following statements is incorrect?

Many people believe that they can tell the difference between Coke and Pepsi.Other people say that the two brands can't be distinguished.To test this,a random sample of 20 adults was selected to participate in a test.After being blindfolded,each person was given a small taste of either Coke or Pepsi and asked to indicate which brand soft drink it was.If people really can't tell the difference,the expected number of correct identifications in the sample would be:

One difference between the binomial distribution and Poisson distribution is that the binomial's upper bound is the number of trials while the Poisson has no particular upper bound.

A sales rep for a national clothing company makes 4 calls per day.Based on historical records,the following probability distribution describes the number of successful calls each day: Based on the information provided,what is the probability of having at least 2 successful calls in one day?

The number of calls to an Internet service provider during the hour between 6:00 and 7:00 p.m.is described by a Poisson distribution with mean equal to 15.Given this information,the expected number of calls in the first 30 minutes is 7.5 calls.

The number of calls to an Internet service provider during the hour between 6:00 and 7:00 p.m.is described by a Poisson distribution with mean equal to 15.Given this information,the standard deviation for the call distribution is about 3.87 calls.

The random variable,number of customers entering a store between 9 AM and noon,is an example of a discrete random variable.

Which of the following statements is true?

Given a binomial distribution with n = 8 and p = 0.40,obtain the probability that the number of successes is within 2 standard deviations of the mean.

The Brockingham Carpet Company prides itself on high quality carpets.At the end of each day,the company quality managers select 3 square yards for inspection.The quality standard requires an average of no more than 2.3 defects per square yard.Last night,the inspector found 8 defects in the sample of 3 square yards.The chance of finding 8 or more defects in the sample is 0.9975.

The probability of the outcome changes from trial to trial in a binomial experiment.

Jennings Assembly in Hartford,Connecticut,uses a component supplied by a company in Brazil.The component is expensive to carry in inventory and consequently is not always available in stock when requested.Furthermore,shipping schedules are such that the lead time for transportation of the component is not a constant.Using historical records,the manufacturing firm has developed the following probability distribution for the product's lead time.The distribution is shown here,where the random variable is the number of days between the placement of the replenishment order and the receipt of the item. What is the coefficient of variation for delivery lead time?

Given a binomial distribution with n = 8 and p = 0.40,obtain the probability that the number of successes is larger than the mean.

A company has 20 cars that are available for use by company executives for official business purposes.Six of these cars are SUVs,8 are luxury type cars,and the rest are basic sedans.Suppose the cars are randomly assigned each week.If 5 cars are put into use,the chance that none of the SUVs or luxury cars will be in the group is approximately .0004.