Exam 5: Discrete Random Variables

In a study conducted for the State Department of Education,30% of the teachers who left teaching did so because they were laid off.Assume that we randomly select 10 teachers who have recently left their profession.Find the probability that exactly 4 of them were laid off.

X has the following probability distribution P(X): Compute the variance value of X.

A fair die is rolled 36 times.What is the standard deviation of the even number (2,4,or 6)outcomes?

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

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 10 customers or less arriving within a minute.

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

Consider the experiment of tossing a fair coin three times and observing the number of heads that result (X = number of heads). Determine the expected number of heads.

In a binomial distribution the random variable X is continuous.

If n = 20 and p = .4,then the mean of the binomial distribution is

Three candidates run for different offices in different counties.Each has a one in three chance of being elected in his/her county.What is the probability that at least one of them will be elected?

Historical data for a local steel manufacturing company shows 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 Poisson distribution. A batch has just been completed.What is the probability that the first three units manufactured in this batch will contain at least a total of 4 defects?

The Securities and Exchange Commission has determined that the number of companies listed in NYSE declaring bankruptcy is approximately a Poisson distribution with a mean of 2.6 per month. Find the probability that exactly 4 bankruptcies occur next month.

It is known that 15% of all college freshmen at Ivey University leave after their first year.Calculate the interval that contains 99.73% of the students who remain if we are looking at a random sample of 300 Ivey University freshmen.

The Post Office has established a record in a major Midwestern city for delivering 90% 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.

The Securities and Exchange Commission has determined that the number of companies listed in NYSE declaring bankruptcy is approximately a Poisson distribution with a mean of 2.6 per month. Find the probability that more than 1 bankruptcy occur next month.

A pharmaceutical company has determined that if a new cholesterol-reducing drug is manufactured (introduced to the market),the following probability distribution will describe this drug's contribution to the company's profits during the next six months. The company management has decided to market this product if the expected contribution to profit for the next six months is more than $90,000.Based on the information given above,should the company begin manufacturing the new drug?

The J.O.Supplies Company buys calculators from a Korean supplier.The probability of a defective calculator is 10%. If 10 calculators are selected at random,what is the probability that 3 or more of the calculators will be defective?

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 five minutes three cars will arrive?

Which one of the following statements is not an assumption of the binomial distribution?

X has the following probability distribution P(X): Compute the expected value of X.