Exam 5: Discrete Probability Distributions

Madam Helga claims to be psychic.A national TV talk personality plans to test her in a live TV broadcast.The process will entail asking Madam Helga a series of 20 independent questions with yes/no answers.The questions would be of the nature that she could not have any way of knowing the answer from prior knowledge.Suppose that Madam Helga correctly answered 15 of the 20 questions,which of the following would be a viable conclusion to reach?

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 more than 4 customers will arrive in a 30-minute period is 0.1933.

Ace Computer Manufacturer buys disk drives in lots of 5,000 units from a supplier in California.The contract calls for,at most,3 percent of the disk drives to be defective.When a shipment arrives,a sample of n = 15 parts is selected.If zero defects are found in this sample,the shipment is accepted.If 3 or more defects are found,the shipment is rejected and sent back to the supplier.If the number of defects found is 1 or 2,a second sample of 15 parts is selected.If this sample yields 1 or fewer defects,the shipment is accepted;otherwise the shipment is rejected.Based on a binomial distribution,the probability that Ace will reject a shipment of parts that meets the contract requirements is approximately 0.0355.

Which of the following statements is true with respect to a Poisson distribution?

The probability function for random variable X is specified as: The expected value of X is

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,how many defects should be expected if 3 containers are inspected?

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 meets the contract requirements will end up being 100 percent inspected is approximately .0746.

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. Calculate the probability that the entire shipment will be kept by Dell even though the shipment has 10% defective microprocessors.

The primary application for the hypergeometric probability distribution is in situations where the sampling is done without replacement from a finite population.

A corporation has 11 manufacturing plants.Of these,7 are domestic and 4 are located outside the United States.Each year a performance evaluation is conducted for 4 randomly selected plants. What is the probability that a performance evaluation will include exactly 1 plant outside the United States?

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.

Explain how to use the binomial distribution table when p,the probability of a success,exceeds 0.50.

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 3-square yard section will contain less than 4 weeds?

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: The expected number of successful sales calls per day is:

A stock portfolio contains 20 stocks.Of these stocks,10 are considered "large-cap" stocks,5 are "mid-cap," and 5 are "small cap." The portfolio manager has been asked by his client to develop a report that highlights 7 randomly selected stocks.When she presents her report to the client,all 7 of the stocks are large-cap stocks.The client is very suspicious that the manager has not randomly selected the stocks.She believes that the chances of all 7 of the stocks being large cap must be very low.Compute the probability of all 7 being large cap.

If a random variable is discrete,it means that the outcome for the random variable can take on only one of two possible values.

A population of 10 items contains 3 that are red and 7 that are green.What is the probability that in a random sample of 3 items selected without replacement,2 red and 1 green items are selected?

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.Suppose 14 people correctly identified the soft drink brand.Which of the following conclusions would be warranted under the circumstance?

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 expected number of defective parts is:

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