Exam 5: Discrete Probability Distributions

A probability distribution with an expected value greater than the expected value of a second probability distribution will also have a higher standard deviation.

The makers of Crustfree Bread in Boston have a quality standard that allows for no more than 3 burned loaves per batch on average.Assuming that the average of 3 per batch is being met,the standard deviation for the number of burned loaves in 4 batches is approximately 1.73 loaves.

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 Vardon Exploration Company is getting ready to leave for South America to explore for oil.One piece of equipment requires 10 batteries that must operate for more than 2 hours.The batteries being used have a 15 percent chance of failing within 2 hours.The exploration leader plans to take 15 batteries.Assuming that the conditions of the binomial apply,the probability that the supply of batteries will not contain enough good ones to operate the equipment is:

Previous research shows that 60 percent of adults who drink non-diet cola prefer Coca-Cola to Pepsi.Recently,an independent research firm questioned a random sample of 25 adult non-diet cola drinkers.That chance that 20 or more of these people will prefer Coca-Cola is:

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 Nationwide Motel Company has determined that 70 percent of all calls for motel reservations request nonsmoking rooms.Recently,the customer service manager for the company randomly selected 25 calls.Assuming that the distribution of calls requesting nonsmoking rooms is described by a binomial distribution,the probability that fewer than 5 customers will request smoking rooms is approximately 0.09.

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 probability of profit being at least $70,000 is 0.65.

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.

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 having at least 2 successful calls in one day?

The only two types of random variables are discrete and continuous random variables.

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?

One of the characteristics of the binomial distribution is that the probability of success for each trial depends on whether the previous trial was a success or not.

The Swanson Auto Body business repaints cars that have been in an accident or which are in need of a new paint job.Its quality standards call for an average of 1.2 paint defects per door panel.Explain why there is a difference between the probability of finding exactly 1 defect when 1 door panel is inspected and finding exactly 2 defects when 2 doors are inspected.

When a single value is randomly chosen from a discrete distribution,the different possible values are mutually exclusive.

The time required to assemble two components into a finished part is recorded for each employee at the plant.The resulting random variable is an example of a continuous random variable.

A local paint store carries 4 brands of paint (W,X,Y,and Z).The store has 5 cans of W,3 cans of X,6 cans of Y,and 15 cans of Z,all in white.It is thought that customers have no preference for one of these brands over another.If this is the case,what is the probability that the next 5 customers will select 1 can of W,X,Y and 2 cans of brand Z?

The number of visible defects on a product container is thought to be Poisson distributed with a mean equal to 3.5.Based on this,the probability that 2 containers will contain a total of less than 2 defects is:

The probability that a product is found to be defective is 0.10.If we examine 50 products,which of the following has the highest probability?

The Nationwide Motel Company has determined that 70 percent of all calls for motel reservations request nonsmoking rooms.Recently,the customer service manager for the company randomly selected 25 calls.Assuming that the distribution of calls requesting nonsmoking rooms is described by a binomial distribution,the expected number of requests for nonsmoking rooms is 14.