Exam 4: Discrete Random Variables

X has the following probability distribution P(X): 1 2 3 4 () .1 .5 .2 .2 -Compute the expected value of X.

If x is a Poisson random variable with a mean of 10,what is the probability that x is greater than or equal to 2?

The hypergeometric distribution is used when sampling _____ replacement from small populations

A courier company has established a record in a major city for delivering 90% of its packages the next working day. -If you send eight local packages,what is the probability that all of them will be delivered the next day.

A local bank has determined that the number of companies listed in the area declaring bankruptcy follows an approximately a Poisson distribution with a mean of 2.6 per year. -Find the probability that more than 1 bankruptcy occurs next year.

Consider the experiment of tossing a fair coin three times and observing the number of heads that result (X = number of heads). -Construct the probability distribution for the random variable X.

Find the probability that x (number of jobs finished on time)is within one standard deviation of the mean.

The distribution whose mean is equal to its variance is the _________ distribution.

The binomial experiment consists of n independent,identical trials,each of which results in either success or failure and is such that the probability of success on any trial is the same.

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?

A manufacturer tested a sample of semiconductor chips and found that 35 were defective and 190 were good.If additional tests are to be conducted with random samples of 160 semiconductor chips,find the mean for the number of defects in these groups of 160 (rounded to nearest whole number).

The requirement that the probability of success remains constant from trial to trial is a property of the _______________ distribution.

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.

The requirement that the probability of success remains constant from trial to trial is a property of the _________________ distribution.

If the probability distribution of X is: () 0 0.1 1 0.2 2 0.3 3 0.4 -What is the variance of X?

The hypergeometric distribution is appropriate when sampling with replacement from small populations

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 standard deviation of X.

If X has the probability distribution

If x is a Poisson random variable with a mean of 10,what is the probability that x is greater than 6?

A vaccine is 95 percent effective. What is the probability that it is not effective for: -One and only one individual out of 20 individuals?