Exam 6: Discrete Probability Distributions

Interpret the Mean of a Discrete Random Variable as an Expected Value -A lab orders a shipment of 100 rats a week, 52 weeks a year, from a rat supplier for experiments that the lab conducts. Prices for each weekly shipment of rats follow the distribution below: Price \ 10.00 \ 12.50 \ 15.00 Probability 0.2 0.3 0.5 How much should the lab budget for next year's rat orders assuming this distribution does not change. (Hint: find the expected price.)

Construct Binomial Probability Histograms -Given that a random variable x, the number of successes, follows a Poisson process, then the probability of success for any two intervals of the same size

Compute the Variance and Standard Deviation of a Discrete Random Variable -The random variable x represents the number of girls in a family of three children. Assuming that boys and girls are equally likely, find the mean and standard deviation for the random variable x.

Compute the Mean and Standard Deviation of a Binomial Random Variable -In a recent survey, 80% of the community favored building a health center in their neighborhood. If 15 citizens are chosen, what is the mean number favoring the health center

Compute Probabilities of a Poisson Random Variable -The university police department must write, on average, five tickets per day to keep department revenues at budgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 9 tickets per day. Find the probability that less than six tickets are written on a randomly selected day from this distribution.

Compute the Mean and Standard Deviation of a Binomial Random Variable -According to government data, the probability that an adult was never in a museum is 13%. In a random survey of 20 adults, what is the mean and standard deviation of the number that were never in a museum

Compute Probabilities of a Poisson Random Variable -Suppose the number of babies born during an eight-hour shift at a hospital s maternity wing follows a Poisson distribution with a mean of 4 an hour. Find the probability that exactly five babies are born during a randomly selected hour.

Construct Probability Histograms -A lab orders a shipment of 100 rats a week, 52 weeks a year, from a rat supplier for experiments that the lab conducts. Prices for each weekly shipment of rats follow the distribution below: Price \ 10.00 \ 12.50 \ 15.00 Probability 0.2 0.15 0.65 Suppose the mean cost of the rats turned out to be $13.63 per week. Interpret this value.

Construct Binomial Probability Histograms -Draw the probability histogram and label the mean for n = 9 and p = 0.7

Compute the Variance and Standard Deviation of a Discrete Random Variable -The random variable x represents the number of computers that families have along with the corresponding probabilities. Find the mean and standard deviation for the random variable $x$ . () 0 0.49 1 0.05 2 0.32 3 0.07 4 0.07

Compute Probabilities of a Poisson Random Variable -The number of traffic accidents that occur on a particular stretch of road during a month follows a Poisson distribution with a mean of 8.9. Find the probability that less than three accidents will occur next month on this stretch of road.

Compute Probabilities of a Poisson Random Variable -The number of road construction projects that take place at any one time in a certain city follows a Poisson distribution with a mean of 2. Find the probability that more than four road construction projects are currently taking place in the city.

Compute the Mean and Standard Deviation of a Binomial Random Variable -The probability that a house in an urban area will develop a leak is 5%. If 20 houses are randomly selected, what is the mean of the number of houses that developed leaks

Compute Probabilities of Binomial Experiments -According to the Federal Communications Commission, 70% of all U.S. households have vcrs. In a random sample of 15 households, what is the probability that at least 13 have vcrs

Compute Probabilities of a Poisson Random Variable -The number of road construction projects that take place at any one time in a certain city follows a Poisson distribution with a mean of 5. Find the probability that exactly three road construction projects are currently taking place in this city.

Determine Whether a Probability Experiment is a Binomial Experiment -If p is the probability of success of a binomial experiment, then the probability of failure is

Compute the Variance and Standard Deviation of a Discrete Random Variable -From the probability distribution, find the mean and standard deviation for the random variable $x$ , which represents the number of bicycles per household in a town of 1000 households. () 0 0.125 1 0.428 2 0.256 3 0.108 4 0.083

Compute Probabilities of a Poisson Random Variable -A history professor finds that when he schedules an office hour at the 10:30 a.m. time slot, an average of three students arrive. Use the Poisson distribution to find the probability that in a randomly selected office hour in the 10:30 a.m. time slot exactly five students will arrive.

Compute Probabilities of a Poisson Random Variable -An online retailer receives an average of five orders per 500 hits on its website. If it gets 100 hits on its website, find the probability of receiving at least two orders. Use the Poisson distribution.

Identify Discrete Probability Distributions -The sum of the probabilities of a discrete probability distribution must be