Exam 6: Discrete Probability Distributions

The number of goals scored at State College hockey games follows a Poisson distribution with a mean of 4goals per game. Find the probability that a randomly selected State College hockey game would have morethan three goals scored.

The university police department keeps track of the number of tickets it write in a year. Last year the campuspolice wrote 1460 tickets. Ticket writing on campus follows a Poisson process. What is the mean number oftickets written per day by the campus police?

Assume that male and female births are equally likely and that the birth of any child does not affect theprobability of the gender of any other children. Suppose that 200 couples each have a baby; find the mean andstandard deviation for the number of boys in the 200 babies.

Suppose x is a random variable for which a Poisson probability distribution with λ = 1.2 provides a goodcharacterization. Find σ for x.

The number of road construction projects that take place at any one time in a certain city follows a Poissondistribution with a mean of 6. Find the probability that more than four road construction projects are currentlytaking place in the city.

Provide an appropriate response. -In an Italian cafe, the following probability distribution was obtained. The random variable x represents thenumber of toppings for a large pizza. Graph the probability histogram. () 0 0.30 1 0.40 2 0.20 3 0.06 4 0.04

A seed company has a test plot in which it is testing the germination of a hybrid seed. They plant 50 rows of 40seeds per row. After a two-week period, the researchers count how many seed per row have sprouted. Theynoted that least number of seeds to germinate was 33 and some rows had all 40 germinate. The germinationdata is given below in the table. The random variable x represents the number of seed in a row thatgerminated and P(x) represents the probability of selecting a row with that number of seed germinating.Determine the mean number of seeds per row that germinated. x 33 34 35 36 37 38 39 40 P(x) 0.02 0.06 0.10 0.20 0.24 0.26 0.10 0.02

Classify the following random variable according to whether it is discrete or continuous. -the number of goals scored in a hockey game

A recent survey found that 70% of all adults over 50 wear sunglasses for driving. In a random sample of 10adults over 50, what is the probability that at least six wear sunglasses?

A psychic network received telephone calls last year from over 1.5 million people. A recent article attempts toshed some light onto the credibility of the psychic network. One of the psychic networkʹs psychics agreed totake part in the following experiment. Five different cards are shuffled, and one is chosen at random. Thepsychic will then try to identify which card was drawn without seeing it. Assume that the experiment wasrepeated 50 times and that the results of any two experiments are independent of one another. If we assumethat the psychic is a fake (i.e., they are merely guessing at the cards and have no psychic powers), find theprobability that they guess at least three correctly.

The number of road construction projects that take place at any one time in a certain city follows a Poissondistribution with a mean of 5. Find the probability that exactly six road construction projects are currentlytaking place in this city.

In a recent survey, 80% of the community favored building a health center in their neighborhood. If 15 citizensare chosen, what is the mean number favoring the health center?

A history professor finds that when he schedules an office hour at the 10:30 a.m. time slot, an average of threestudents arrive. Use the Poisson distribution to find the probability that in a randomly selected office hour inthe 10:30 a.m. time slot exactly seven students will arrive.

An electronics store receives a shipment of 50 flat screen TVs of which 5 are defective. During the qualitycontrol inspection, 4 TVs are selected at random from the shipment for testing. The random variable Xrepresents the number of defective computers in the sample

Consider the discrete probability distribution to the right when answering the following question. Find theprobability that x exceeds 4. x 2 4 6 8 P(x) 0.03 ? 0.08 0.31

According to the Federal Communications Commission, 70% of all U.S. households have vcrs. In a randomsample of 15 households, what is the probability that at least 13 have vcrs?

N=130, n=10, k=35

A seed company has a test plot in which it is testing the germination of a hybrid seed. They plant 50 rows of 40seeds per row. After a two-week period, the researchers count how many seed per row have sprouted. Theynoted that least number of seeds to germinate was 33 and some rows had all 40 germinate. The germinationdata is given below in the table. The random variable x represents the number of seed in a row thatgerminated and P(x) represents the probability of selecting a row with that number of seed germinating.Determine the standard deviation of the number of seeds per row that germinated. x 33 34 35 36 37 38 39 40 P(x) 0.02 0.06 0.10 0.20 0.24 0.26 0.10 0.02

A history professor decides to give a 12-question true-false quiz. She wants to choose the passing grade suchthat the probability of passing a student who guesses on every question is less than 0.10. What score should beset as the lowest passing grade?

In a carnival game, a person wagers $2 on the roll of two dice. If the total of the two dice is 2, 3, 4, 5, or 6 thenthe person gets $4 (the $2 wager and $2 winnings). If the total of the two dice is 8, 9, 10, 11, or 12 then theperson gets nothing (loses $2). If the total of the two dice is 7, the person gets $0.75 back (loses $0.25). What isthe expected value of playing the game once?