Exam 6: Discrete Probability Distributions

Compute the Probabilities of Hypergeometric Experiments -Among the contestants in a competition are 35 women and 21 men. If 5 winners are randomly selected, what is the probability that they are all men

Construct Probability Histograms -In an Italian cafe, the following probability distribution was obtained. The random variable $x$ represents the number 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

Determine Whether a Probability Experiment is a Binomial Experiment -Decide whether the experiment is a binomial experiment. If it is not, explain why. You observe the gender of the next 950 babies born at a local hospital. The random variable represents the number of boys.

Determine Whether a Probability Experiment is a Hypergeometric Experiment -An electronics store receives a shipment of 47 flat screen TVs of which 10 are defective. During the quality control inspection, $4 \mathrm { TVs }$ are selected at random from the shipment for testing. The random variable $\mathrm { X }$ represents the number of defective computers in the sample

Compute Probabilities of a Poisson Random Variable -Suppose the number of babies born during an 8-hour shift at a hospital s maternity wing follows a Poisson distribution with a mean of 7 an hour. Find the probability that three babies are born during a particular 1-hour period in this maternity wing.

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

Compute the Mean and Standard Deviation of a Hypergeometric Random Variable - $\mathrm { N } = 140 , \mathrm { n } = 10 , \mathrm { k } = 30$

Identify Discrete Probability Distributions -An Apple Pie Company knows that the number of pies sold each day varies from day to day. The owner believes that on $50 \%$ of the days she sells 100 pies. On another $25 \%$ of the days she sells 150 pies, and she sells 200 pies on the remaining $25 \%$ of the days. To make sure she has enough product, the owner bakes 200 pies each day at a cost of $\$ 1.50$ each. Assume any pies that go unsold are thrown out at the end of the day. If she sells the pies for $\$ 4$ each, find the probability distribution for her daily profit.

Compute Probabilities of Binomial Experiments -According to insurance records a car with a certain protection system will be recovered 95% of the time. Find the probability that 5 of 8 stolen cars will be recovered.

Determine Whether a Probability Experiment is a Binomial Experiment -Decide whether the experiment is a binomial experiment. If it is not, explain why. Selecting five cards, one at a time without replacement, from a standard deck of cards. The random variable is the number of picture cards obtained.

Classify the following random variable according to whether it is discrete or continuous -The number of violent crimes committed in a day possesses a distribution with a mean of 1.3 crimes per day and a standard deviation of four crimes per day. A random sample of 120 days was observed, and the sample mean number of crimes for the sample was calculated. The data that was collected in this experiment could be measured with a __________ random variable.

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 6.6. Find the probability that the next two months will both result in four accidents each occurring on this stretch of road.

Compute Probabilities of Binomial Experiments -A quiz consists of 10 true or false questions. To pass the quiz a student must answer at least eight questions correctly. If the student guesses on each question, what is the probability that the student will pass the quiz

Compute the Variance and Standard Deviation of a Discrete Random Variable -A baseball player is asked to swing at pitches in sets of four. The player swings at 100 sets of 4 pitches. The probability distribution for hitting a particular number of pitches is given below. Determine the standard deviation for this discrete probability distribution. x 0 1 2 3 4 P(x) 0.02 0.07 0.22 0.27 0.42

Determine Whether a Probability Experiment is a Binomial Experiment -Decide whether the experiment is a binomial experiment. If it is not, explain why. Survey 50 investors to see how many different stocks they own. The random variable represents the number of different stocks owned by each investor.

Determine Whether a Probability Experiment is a Binomial Experiment -Which of the below is not a requirement for binomial experiment

Compute Probabilities of a Poisson Random Variable -A help desk receives an average of four calls per hour on its toll-free number. For any given hour, find the probability that it will receive exactly seven calls. Use the Poisson distribution.

Determine Whether a Probability Experiment is a Binomial Experiment -Decide whether the experiment is a binomial experiment. If it is not, explain why. You draw a marble 300 times from a bag with three colors of marbles. The random variable represents the color of marble that is drawn.

Compute Probabilities of Binomial Experiments -The probability that a house in an urban area will develop a leak is 5%. If 23 houses are randomly selected, what is the probability that none of the houses will develop a leak

Construct Probability Histograms -The random variable x represents the number of boys in a family of three children. Assuming that boys and girls are equally likely, (a) construct a probability distribution, and (b) graph the probability histogram.