Exam 5: Discrete Probability Distributions

Dell Computers receives large shipments of microprocessors from Intel Corp.It must try to ensure the proportion of microprocessors that are defective is small.Suppose Dell decides to test five microprocessors out of a shipment of thousands of these microprocessors.Suppose that if at least one of the microprocessors is defective,the shipment is returned. If Intel and Dell agree that Intel will not provide more than 5% defective chips,calculate the probability that the entire shipment will be returned even though only 5% are defective.

A random variable is generated when a variable's value is determined by using classical probability.

A pizza restaurant uses 7 different toppings on its pizzas.At lunch time it has a pizza buffet and makes pizzas with 2 toppings.If it wants to serve every possible combination of 2 toppings,it would need to make 14 different pizzas.

If a binomial distribution applies with a sample size of n = 20,find the probability of at least 7 successes if the probability of a success is 0.25.

If a binomial distribution applies with a sample size of n = 20,find the expected value,n = 20,p = 0.20.

Because of bad weather,the number of days next week that the captain of a charter fishing boat can leave port is uncertain.Let x = number of days that the boat is able to leave port per week.The following probability distribution for the variable,x,was determined based on historical data when the weather was poor: Based on the probability distribution,what is the expected number of days per week the captain can leave port?

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.

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 all 3 parts are from the Wilson Company is approximately .1958.

The manager for State Bank and Trust has recently examined the credit card account balances for the customers of her bank and found that 20% have an outstanding balance at the credit card limit.Suppose the manager randomly selects 15 customers and finds 4 that have balances at the limit.Assume that the properties of the binomial distribution apply. What is the probability that 4 or fewer customers in the sample will have balances at the limit of the credit card?

The manager for State Bank and Trust has recently examined the credit card account balances for the customers of her bank and found that 20% have an outstanding balance at the credit card limit.Suppose the manager randomly selects 15 customers and finds 4 that have balances at the limit.Assume that the properties of the binomial distribution apply. What is the probability of finding 4 customers in a sample of 15 who have "maxed out" their credit cards?

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.

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 Weyerhauser Lumber Company headquartered in Tacoma,Washington,is one of the largest timber and wood product companies in the world.Weyerhauser manufactures plywood at one of its Oregon plants.Plywood contains minor imperfections that can be repaired with small "plugs." One customer will accept plywood with a maximum of 3.5 plugs per sheet on average.Suppose a shipment was sent to this customer and when the customer inspected two sheets at random,10 plugged defects were counted.What is the probability of observing 10 or more plugged defects if in fact the 3.5 average per sheet is being satisfied?

The Hawkins Company randomly samples 10 items from every large batch before the batch is packaged and shipped.According to the contract specifications,5 percent of the items shipped can be defective.If the inspectors find 1 or fewer defects in the sample of 10,they ship the batch without further inspection.If they find 2 or more,the entire batch is inspected.Based on this sampling plan,the probability that a batch that contains twice the amount of defects allowed by the contract requirements will be shipped without further inspection is approximately .3874.

The following probability distribution has been assessed for the number of accidents that occur in a Midwestern city each day: Based on this probability distribution,the standard deviation in the number of accidents per day is:

Magic Valley Memorial Hospital administrators have recently received an internal audit report that indicates that 15% of all patient bills contain an error of one form or another.After spending considerable effort to improve the hospital's billing process,the administrators are convinced that things have improved.They believe that the new error rate is somewhere closer to 0.05.Suppose that recently the hospital randomly sampled 10 patient bills and conducted a thorough study to determine whether an error exists.It found 3 bills with errors.Assuming that managers are correct that they have improved the error rate to 0.05,what is the probability that they would find 3 or more errors in a sample of 10 bills?

A package delivery service claims that no more than 5 percent of all packages arrive at the address late.Assuming that the conditions for the binomial hold,if a sample of size 10 packages is randomly selected,and the 5 percent rate holds,what is the probability that exactly 2 packages in the sample arrive late?

If the number of defective items selected at random from a parts inventory is considered to follow a binomial distribution with n = 50 and p = 0.10,the standard deviation of the number of defective parts is:

The hypergeometric probability distribution is used rather than the binomial or the Poisson when:

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: