Exam 5: Discrete Random Variables

Your company's internal auditor believes that 10% of the company's invoices contain errors.To check this theory,20 invoices are randomly selected and 5 are found to have errors. Would you accept or reject the claim?

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

Assume the number of trucks passing an intersection has a Poisson distribution with mean of 5 trucks per minute.What is the probability of 0 or 1 trucks in one minute?

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

Consider a Poisson distribution with an average of 3 customers per minute at the local grocery store: 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 variance of X.

If X has the probability distribution compute the expected value of X.

According to data from the state blood program,40% of all individuals have group A blood.If six (6)individuals give blood,find the probability Suppose that of the six randomly selected individuals,3 have group A blood.Would you believe the data from the state blood program?

If the probability distribution of X is: What is the variance of X?

The mean of the binomial distribution is equal to:

Historical data shows that the average number of patient arrivals at the intensive care unit of General Hospital is 3 patients every 2 hours.Assume that the patient arrivals are distributed according to Poisson distribution. Determine the probability of 6 patients arriving in a five-hour period.

For a binomial process,the probability of success is 40% and the number of trials is 5. Find P(X $\le$ 1).

A discrete random variable may assume a countable number of outcome values.

Your company's internal auditor believes that 10% 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 written,five or more would contain errors if the theory is valid?

If the probability of a success on a single trial is .2,what is the probability of obtaining 3 successes in 10 trials if the number of successes is binomial?

Which of the following is a valid probability value for a discrete random variable?

During off hours,cars arrive at a tollbooth on the East-West toll road at an average rate of 0.5 cars per minute.The arrivals are distributed according to the Poisson distribution. What is the probability that during the next minute three cars will arrive?

A random variable is said to be discrete if

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

Which of the following distributions can be used to solve the following problem? The average number of cars arriving at a drive-thru fast food restaurant is 3 in ten minutes,what is the probability that exactly 4 cars will arrive in a five minute interval?

Twenty coins are tossed.What is the probability of getting exactly 10 heads?