Exam 5: Discrete Random Variables

In a hypergeometric probability distribution of a population of N items,r refers to the number of successes and N - r to the number of failures.

A test has 6 multiple choice questions,each with 4 alternatives.What is the probability of guessing 5 or more questions correctly?

A hypergeometric random variable x has a distribution that is approximated by a binomial distribution when:

One die is thrown.What is the expected value of the number of dots on the top face of the die?

Your company's internal auditor believes that 10 percent of the company's invoices contain errors.To check this theory,20 invoices are randomly selected,and 5 are found to have errors.What is the probability that of the 20 invoices selected,5 or more would contain errors if the theory is valid?

A study conducted by a local university found that 25 percent of college freshmen support increased spending on environmental issues.If 6 college freshmen are randomly selected,find the probability that fewer than 4 support increased spending on environmental issues.

Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store.If X = the number of arrivals per minute,find the probability of more than 7 customers arriving within a minute.

Consider a Poisson distribution with an average of 4 customers per minute at the local grocery store.If X = the number of arrivals per minute,find the standard deviation of X.

The J.O.Supplies Company buys calculators from a Korean supplier.The probability of a defective calculator is 10 percent.If 100 calculators are selected at random,what is the expected number of defectives?

Historical data for a local steel manufacturing company show that the average number of defects per standard sheet of steel is 2.In addition,the number of defects per unit is distributed according to a Poisson distribution.Determine the standard deviation of the number of defects for 32 sheets of metal.

The probability that a given computer chip will fail is 0.02.Find the probability that of 5 delivered chips,exactly 2 will fail.

The time (in seconds)it takes for an athlete to run 50 meters is an example of a continuous random variable.

Suppose that x has a hypergeometric distribution with N = 10,r = 5,and n = 3.Calculate the standard deviation of the distribution.

The manager of the local grocery store has determined that,on average,4 customers use the service desk every half-hour.Assume that the number of customers using the service desk has a Poisson distribution.What is the probability that during a randomly selected half-hour period,exactly 2 customers use the service desk?

If x is a Poisson random variable with a mean of 10,what is the probability that x is equal to 8?

If in a hypergeometric distribution r is 300,N = 600,and n = 30,estimate the binomial probability of success.

A correlation coefficient is a unitless measure of the linear relationship between two random variables.

The manager of the local grocery store has determined that,on average,4 customers use the service desk every half-hour.Assume that the number of customers using the service desk has a Poisson distribution.What is the probability that during a randomly selected half-hour period,no more than 2 customers use the service desk?

Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store.If X = the number of arrivals per minute,find the probability of 3 customers arriving within a minute.

The Post Office has established a record in a major midwestern city for delivering 90 percent of its local mail the next working day.If you mail eight local letters,what is the probability that all of them will be delivered the next day?