Exam 6: Random Variables and Discrete Probability Distributions

The binomial random variable is the number of successes that occur in a fixed period of time.

For a random variable X , if V ( cX )= 4 V ( X ), where V refers to the variance, then c must be 2.

Unsafe Levels of Radioactivity The number of incidents at a nuclear power plant has a Poisson distribution with a mean of 6 incidents per year. {Unsafe Levels of Radioactivity Narrative} Find the probability that there will be at least 3 incidents in a year.

If n = 10 and p = 0.60, then the mean of the binomial distribution is

The probability P ( X £ x )is called a(n)____________________ probability. The binomial table reports these probabilities.

Sports Fans Suppose that past history shows that 5% of college students are sports fans. A sample of 10 students is to be selected. {Sports Fans Narrative} Find the probability that at most 1 student is a sports fan.

The variance of a binomial distribution is equal to ____________________.

Retries The following table contains the probability distribution for X = the number of retries necessary to successfully transmit a 1024K data package through a double satellite media. {Retries Narrative} What is the probability of a least one retry?

In a Poisson distribution, the mean and standard deviation are equal.

Post Office The number of arrivals at a local post office between 3:00 and 5:00 P.M. has a Poisson distribution with a mean of 12. {{Post Office Narrative} Find the probability that the number of arrivals between 4:00 and 5:00 P.M. is exactly two.

Sports Fans Suppose that past history shows that 5% of college students are sports fans. A sample of 10 students is to be selected. {Sports Fans Narrative} A sample of 100 students is to be selected. What is the standard deviation of the number of sports fans you expect?

A binomial experiment consists of a(n)____________________ number of trials, n .

Sports Fans Suppose that past history shows that 5% of college students are sports fans. A sample of 10 students is to be selected. {Sports Fans Narrative} Find the probability that less than 1 student is a sports fan.

The binomial distribution deals with consecutive trials, each of which has two possible outcomes.

The number of days that a microcomputer goes without a breakdown is an example of a(n)____________________ random variable.

Online Bankers An official from the securities commission estimates that 75% of all online bankers have profited from the use of insider information. Assume that 15 online bankers are selected at random from the commission's registry. {Online Bankers Narrative} What is the expected number of Online bankers who have profited from the use of insider information?

Faculty rank (professor, associate professor, assistant professor, and lecturer)is an example of a discrete random variable.

Shopping Outlet A shopping outlet estimates the probability distribution of the number of stores shoppers actually enter as shown in the table below. {Shopping Outlet Narrative} Find the expected value of the number of stores entered.

A motorcycle insurance company evaluates many numerical variables about a person before deciding on an appropriate rate for motorcycle insurance. The number of tickets a person has received in the last 3 years is an example of a(n)____________________ random variable.

911 Phone Calls 911 phone calls arrive at the rate of 30 per hour at the local call center. {911 Phone Calls Narrative} Find the probability of receiving exactly eight calls in 15 minutes.