Exam 5: Discrete Probability Distributions

In a Florida town,the probability distribution for the number of legitimate emergency calls per day for the Fire Department is given as follows.Also shown is the probability distribution for the number of false alarms: Given this information,the expected number of total calls to the fire department is 1.60 calls.

The following probability distribution has been assessed for the number of accidents that occur in a Midwestern city each day: This distribution is an example of:

The number of weeds that remain living after a specific chemical has been applied averages 1.3 per square yard and follows a Poisson distribution.Based on this,what is the probability that a 1-square yard section will contain less than 4 weeds?

The number of customers who arrive at a fast food business during a one-hour period is known to be Poisson distributed with a mean equal to 8.60.The probability that exactly 8 customers will arrive in a one-hour period is 0.1366.

The Ace Construction Company has entered into a contract to widen a street in Boston.The possible payoffs for this project have been determined by management.The probabilities for these payoffs could be determined using a binomial distribution.

The graph of a discrete random variable looks like a histogram where the probability of each possible outcome is represented by a bar.

The number of no-shows for dinner reservations at the Cottonwood Grille is a discrete random variable with the following probability distribution: Based on this information,the most likely number of no-shows on any given day is 0 customers.

The Cromwell Construction Company has the opportunity to enter into a contract to build a mountain road.The following table shows the probability distribution for the profit that could occur if it takes the contract: Based on this information,the profit standard deviation for the company if it takes the contract is $11,235.

Arrivals to a bank automated teller machine (ATM)are distributed according to a Poisson distribution with a mean equal to three per 15 minutes. What is the probability that fewer than four customers will arrive in a 30-minute segment?

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 this information,the probability that the sales rep will have a total of 2 successful calls in a two-day period is:

John Thurgood founded a company that translates Chinese books into English.His company is currently testing a computer-based translation service.Since Chinese symbols are difficult to translate,John assumes the computer program will make some errors,but then so do human translators.The computer error rate is supposed to be an average of 3 per 400 words of translation.Suppose John randomly selects a 1,200-word passage.Assuming that the Poisson distribution applies,if the computer error rate is actually 3 errors per 400 words,calculate the probability that more than 14 errors will be found.

Which of the following is not a condition of the binomial distribution?

A new phone answering system installed by the Ohio Power Company is capable of handling five calls every 10 minutes.Prior to installing the new system,company analysts determined that the incoming calls to the system are Poisson distributed with a mean equal to two every 10 minutes.If this incoming call distribution is what the analysts think it is,what is the probability that in a 10-minute period more calls will arrive than the system can handle?

The Cromwell Construction Company has the opportunity to enter into a contract to build a mountain road.The following table shows the probability distribution for the profit that could occur if it takes the contract: Based on this information,the expected profit for the company if it takes the contract is $70,500.

A small city has two taxi companies (A and B).Each taxi company has 5 taxis.A motel has told these companies that they will randomly select a taxi company when one of its customers needs a cab.This morning 3 cabs were needed.Assuming that no one individual taxi can be used more than once,what is the probability that 2 of the cabs selected will be from Company A and the other will be from B?

The Ski Patrol at Criner Mountain Ski Resort has determined the following probability distribution for the number of skiers that are injured each weekend: Based on this information,the expected number of injuries per weekend is 2.25.

College-Pro Painting does home interior and exterior painting.The company uses inexperienced painters that do not always do a high-quality job.It believes that its painting process can be described by a Poisson distribution with an average of 4.8 defects per 400 square feet of painting. What is the probability that six randomly sampled sections of size 400 square feet will each have 7 or fewer blemishes?

College-Pro Painting does home interior and exterior painting.The company uses inexperienced painters that do not always do a high-quality job.It believes that its painting process can be described by a Poisson distribution with an average of 4.8 defects per 400 square feet of painting. What is the probability that a 400-square-foot painted section will have fewer than 6 blemishes?

The mean number of errors per page made by a member of the word processing pool for a large company is thought to be 1.5 with the number of errors distributed according to a Poisson distribution.If three pages are examined,what is the probability that more than 3 errors will be observed?

Which of the following is true with respect to the binomial distribution?