Exam 6: Discrete Probability Distributions

A recent article in the paper claims that government ethics are at an all-time low. Reporting on a recent sample,the paper claims that 38% of all constituents believe their representative possesses low ethical standards.Assume that responses were randomly and independently collected. A representative of a district with 1,000people does not believe the paperʹs claim applies to her. If the claim is true, how many of the representativeʹsconstituents believe the representative possesses low ethical standards?

The university police department must write, on average, five tickets per day to keep department revenues atbudgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of 5tickets per day. Find the probability that exactly eight tickets are written on a randomly selected day from thisdistribution.

The random variable x represents the number of computers that families have along with the correspondingprobabilities. 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

The university police department must write, on average, five tickets per day to keep department revenues atbudgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of6.5 tickets per day. Interpret the value of the mean.

The number of traffic accidents that occurs on a particular stretch of road during a month follows a Poissondistribution with a mean of 6.3. Find the probability that less than two accidents will occur on this stretch ofroad during a randomly selected month.

Classify the following random variable according to whether it is discrete or continuous. -the heights of the bookcases in a school library

From the probability distribution, find the mean and standard deviation for the random variable x, whichrepresents the number of bicycles per household in a town of 1000 households. x P(x) 0 0.125 1 0.428 2 0.256 3 0.108 4 0.083

A university must choose a team of 5 students to participate in a TV quiz show. The students will be chosen atrandom from a pool of 44 potential participants of whom 20 are women. The random variable X represents thenumber of women on the team.

A quiz consists of 10 true or false questions. To pass the quiz a student must answer at least eight questionscorrectly. If the student guesses on each question, what is the probability that the student will pass the quiz?

In a recent survey, 72% of the community favored building a health center in their neighborhood. If 14 citizensare chosen, find the probability that exactly 10 of them favor the building of the health center.

Classify the following random variable according to whether it is discrete or continuous. -the pressure of water coming out of a fire hose

A dice game involves throwing three dice and betting on one of the six numbers that are on the dice. The gamecosts $6 to play, and you win if the number you bet appears on any of the dice. The distribution for theoutcomes of the game (including the profit) is shown below: Number of dice with your number Profit Probability of Observing 0 -\ 6 125/216 1 \ 6 75/216 2 \ 8 15/216 3 \ 18 1/216 Find your expected profit from playing this game.

The probability that a house in an urban area will develop a leak is 4%. If 39 houses are randomly selected,what is the probability that none of the houses will develop a leak?

In a sandwich shop, the following probability distribution was obtained. The random variable x represents thenumber of condiments used for a hamburger. Find the mean and standard deviation for the random variable x. () 0 0.30 1 0.40 2 0.20 3 0.06 4 0.04

In a lottery, a player selects six numbers between 1 and 36 inclusive. The six winning numbers (all different) areselected at random from the numbers 1-36. To win a prize, the player must match three or more of the winningnumbers. What is the probability that the player matches exactly 3 numbers?

Fifty percent of the people that use the Internet order something online. Find the probability that only five of 8Internet users will order something online.

The probability that an individual has 20-20 vision is 0.1. In a class of 10 students, what is the mean andstandard deviation of the number with 20-20 vision in the class?

The university police department must write, on average, five tickets per day to keep department revenues atbudgeted levels. Suppose the number of tickets written per day follows a Poisson distribution with a mean of9.6 tickets per day. Find the probability that less than six tickets are written on a randomly selected day fromthis distribution.

The owner of a farmerʹs market was interested in determining how many oranges a person buys when theybuy oranges. He asked the cashiers over a weekend to count how many oranges a person bought when theybought oranges and record this number for analysis at a later time. The data is given below in the table. Therandom variable x represents the number of oranges purchased and P(x) represents the probability that acustomer will buy x oranges. Determine the variance of the number of oranges purchased by a customer. x 1 2 3 4 5 6 7 8 9 10 P(x) 0.05 0.19 0.20 0.25 0.12 0.10 0 0.08 0 0.01

Classify the following random variable according to whether it is discrete or continuous. -the speed of a car on a New York tollway during rush hour traffic