Exam 6: Random Variables and Discrete Probability Distributions

Number of Horses The random variable X represents the number of horses per family in a rural area in Iowa, with the probability distribution: p ( x )= 0.05 x , x = 2, 3, 4, 5, or 6. {Number of Horses Narrative} Find the following probabilities:

The monthly sales at a Gas Station have a mean of $50,000 and a standard deviation of $6,000. Profits are calculated by multiplying sales by 40% and subtracting fixed costs of $12,000. Find the mean and standard deviation of monthly profits.

For a random variable X , E ( X + 2)- 5 = E ( X )- 3, where E refers to the expected value.

The mean of a Poisson distribution, where m is the average number of successes occurring in a specified interval, is m .

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} Calculate the expected value of Y directly from the probability distribution of Y .

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 least 1 student is a sports fan.

In the Poisson distribution, the ____________________ is equal to the variance.

The variance of a binomial distribution for which n = 100 and p = 0.20 is:

The Sutton police department must write, on average, 6 tickets a day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 6.5 tickets per day. Interpret the value of the mean.

On the average, 1.6 customers per minute arrive at any one of the checkout counters of Sunshine food market. What type of probability distribution can be used to find out the probability that there will be no customers arriving at a checkout counter in 10 minutes?

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} Find the variance and standard deviation of the number of Online bankers who have profited from the use of insider information.

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 3:30 and 4:00 P.M. is at least 10.

Number of Motorcycles The probability distribution of a discrete random variable X is shown below, where X represents the number of motorcycles owned by a family. {Number of Motorcycles Narrative} Find the expected value of X .

Another name for the mean of a probability distribution is its expected value.

Suppose that the number of buses arriving at a Depot per minute is a Poisson process. If the average number of buses arriving per minute is 3, what is the probability that exactly 6 buses arrive in the next minute?

A continuous variable may take on any value within its relevant range even though the measurement device may not be precise enough to record it.

Gym Visits Let X represent the number of times a student visits a gym in a one month period. Assume that the probability distribution of X is as follows: {Gym Visits Narrative} Find the mean m and the standard deviation s of this distribution.

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 exactly 1 student is a sports fan.

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} Use the laws of variance to calculate the variance and standard deviation of Y from the probability distribution of X .

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 average number that you would expect to sports fan?