Exam 6: Modeling Random Events: the Normal and Binomial Models

Use the following information for the question. The average travel time to work for a person living and working in Kokomo,Indiana is 17 minutes. Suppose the standard deviation of travel time to work is 4.5 minutes and the distribution of travel timeis approximately normally distributed. - Which of these statements is asking for a measurement (i. e. is an inverse normal question)?

Five identical poker chips are tossed in a hat and mixed up. Two of the chips have been marked with an X to indicate that if drawn a valuable prize will be awarded. If you and two of your friends Each draws a chip (with replacement), what is the probability that at least one of your group of Three will win the valuable prize? Round to the nearest thousandth.

At a county animal shelter, the probability that a stray cat comes into the shelter withrabies is 0.145 and the probability that a stray dog comes into the shelter with rabies is0.157. A volunteer at the shelter records whether the next thirty cats or dogs delivered tothe shelter has rabies. Which of the condition or conditions for use of the binomial model isor are not met?

Use the following information for the question. The average travel time to work for a person living and working in Kokomo,Indiana is 17 minutes. Suppose the standard deviation of travel time to work is 4.5 minutes and the distribution of travel timeis approximately normally distributed. -Suppose that it is reported in the news that 8% of the people living and working in Kokomo feel"very satisfied" with their commute time to work. What is the travel time to work that separates thebottom 8% of people with the shortest travel times and the upper 92%? Round to the nearest tenthof a minute.

Determine whether the variable would best be modeled as continuous or discrete: The number of tomatoes harvested each week from a greenhouse tomato plant.

List the four characteristics of the binomial model.

A suit of standard playing cards has thirteen cards. Suppose the suit of hearts is thoroughlyshuffled and that you have the opportunity to play the following game: You win $10 if youchoose the ten or queen of hearts, you lose $5 if you choose the jack or king of hearts, youwin $2 if you choose the five or seven of hearts, and you lose $10 if you choose the ace ofhearts. With any other outcome you will win or lose nothing. Complete the table thatshows the probability distribution. Would it be sensible to play this game? Winnings Probability +\ 10 -\ 5 +\ 2 -\ 10 0

Use the following information for the question. Male players at the high school, college and professional ranks use a regulation basketball that weighs 22.0 ounces with a standard deviation of 1.0 ounce. Assume that the weights of basketballs are approximately normally distributed -Would it be unusual to randomly select a regulation basketball and find that it weighs 23.75 ounces?

An MP3 playlist, containing several songs from five genres, is set to shuffle. The following table shows the genre and the associated probability for the first song played. Does the table represent a Probability distribution?

Suppose the probability that a person does not recycle is 0.23. If 300 randomly selectedpeople were asked "Do you recycle? " would you be surprised if 65 said no to this question? Why?

Use the following information for the question. Suppose that the probability that the train travelling from Holland, Michigan to Chicago, Illinois arrives on time is 0.80. For the questions that follow, consider a sample of twenty randomly selected train trips. -What is the probability that at least nineteen trips out of twenty arrive to Chicago on time? Round to the nearest thousandth.

Use the following information to answer the question. Suppose that the probability that a person books an airline ticket using an online travel website is 0.72. For the questions that follow, consider a sample of ten randomly selected people who recently booked an airline ticket. -What is the probability that no more than three out of ten people used an online travel websitewhen they book their airline ticket? Round to the nearest thousandth.

Use the following information for the question. Male players at the high school, college and professional ranks use a regulation basketball that weighs 22.0 ounces with a standard deviation of 1.0 ounce. Assume that the weights of basketballs are approximately normally distributed. -Roughly what percentage of regulation basketballs weigh more than 23.1 ounces? Round to thenearest tenth of a percent.

Use the following information to answer the question. Suppose that weights of jars of Puff brand marshmallow cream has apopulation mean of 24.5 ounces and a population standard deviation of 0.19 ounces and are approximately normallydistributed. Use the figure below to find determine the specified probabilities. -What is the probability that a randomly selected jar of Puff marshmallow cream will begreater than 24.45 ounces? What is the probability that a randomly selected jar of Puffmarshmallow cream will be less than 24.22 ounces? Round to the nearest thousandth.

List two requirements that must be satisfied for any probability distribution. Explain howthe probability distribution in question (4) satisfies these requirements.

Determine whether the variable would best be modeled as continuous or discrete: The temperatureof a cup of coffee dispensed from a beverage vending machine, taken four times during a 24-hourperiod.

Suppose that the probability that a person between the ages of 19 and 24 checks their dailyhoroscope is 0.12. If 400 randomly selected people between the ages of 19 and 24 were asked "Doyou check your daily horoscope?", would you be surprised if 63 or more said yes to this question?Why?

Use the following information for the question. Suppose that the probability that the train travelling from Holland, Michigan to Chicago, Illinois arrives on time is 0.80. For the questions that follow, consider a sample of twenty randomly selected train trips. -Approximately how many trips would you expect to arrive on time out of twentyrandomly selected trips, give or take how many trips? Round to the nearest whole trip.

The normal modelN(58, 21) describes the distribution of weights of chicken eggs in grams.Suppose that the weight of a randomly selected chicken egg has a z-score of-2.01. What is theweight of this egg in grams? Round to the nearest hundredth of a gram.

Which of the following characteristics are notrequired for the binomial model?