Exam 4: Discrete Random Variables

If the number of surface nonconformities on a specific size of a metal piece is the discrete random variable in question,then the appropriate probability distribution that can describe the probability of a specific size metal sheet containing 3 nonconformities is most likely given by the binomial distribution.

Which of the following statements about the binomial distribution is not correct?

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 expected value of X.

An urn contains 50 black balls and 20 blue balls.If you select 30 balls at random,what is the expected number of black balls?

When using hypergeometric distribution,it is assumed that the trials are __________ and the probability of success ________ from trial to trial.

For a binomial experiment, the probability of success is 40% and the number of trials is 5. Let X represent the number of successes. -Find the expected value of X.

A random variable is said to be discrete if

Find the probability of 3 customers arriving within a minute.

According to data from a federal blood program, 40% of all individuals have type A blood. If six individuals give blood, find the probability -Exactly three of the individuals has type A blood?

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?

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 no more than one bankruptcy occurs next year.

Two characteristics/assumptions of the Poisson distribution include:

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

If you roll a die 20 times,the number of times you roll a six is an example of a ________ random variable.

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

For a binomial experiment, the probability of success is 40% and the number of trials is 5. Let X represent the number of successes. -Find the standard deviation of X.

The number of calls coming into a PBX follows a Poisson process with a mean of 120 calls per hour.What is the probability of no calls in a one-minute interval?

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

In a study conducted for a local union,30% of the employees who became unemployed in the last year did so because they were laid off.Assume that we randomly select 10 employees who have recently left their position.Find the probability that exactly 4 of them were laid off.

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