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 time is approximately normally distributed. -Suppose that it is reported in the news that 12% of the people living and working in Kokomo feel that their commute is too long. What is the travel time to work that separates the top 12% of people with the longest travel times and the lower 88%? Round to the nearest tenth of a minute.

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 at least nine out of ten people used an online travel website when they booked their airline ticket? Round to the nearest thousandth.

The normal model N(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 the weight of this egg in grams? Round to the nearest hundredth of a gram.

At a county animal shelter, the probability that a stray cat comes into the shelter with rabies is 0.145 and the probability that a stray dog comes into the shelter with rabies is 0.157. A volunteer at the shelter records whether the next thirty cats or dogs delivered to the shelter has rabies. Which of the condition or conditions for use of the binomial model is or are not met?

Which of the following characteristics are not required for the binomial model?

When exposed to heat, the reaction time of a certain chemical always occurs after thirteen minutes, but before 17 minutes. Reaction times for this chemical can be modeled by a uniform distribution, that is, the reaction time is just as likely to occur at thirteen minutes as it is to occur at seventeen minutes. Find the probability that the reaction will happen after fifteen minutes. Shade the appropriate area and calculate the numerical value of the probability.

Determine which of the given procedures describe a binomial distribution.

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 thirteen or less trips out of twenty arrive on time to Chicago? Round to the nearest thousandth.

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 time is approximately normally distributed. -Approximately what percentage of people living and working in Kokomo have a travel time to work that is at least 20 minutes? Round to the nearest whole percent.

List the four characteristics of the binomial model.

Use the following information for the question. On a busy day, the average roller coaster wait time at a large amusement park is 27 minutes. Suppose the standard deviation of wait time is 11.9 minutes and the distribution of wait times is approximately normally distributed. -To improve customer satisfaction, the amusement park manager has decided to give food coupons to customers with long wait times. The manager decides to give the coupons to the top 10% of people waiting the longest. What is the minimum wait time for the top 10%? Round to the nearest tenth of a minute.

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 exactly fifteen trips out of twenty will arrive in Chicago on time? Round to the nearest thousandth.

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 website when they book their airline ticket? Round to the nearest thousandth.

Use the following information to answer the question. Suppose that the probability that a person books a hotel using an online travel website is 0.68. For the questions that follow, consider a sample of fifteen randomly selected people who recently booked a hotel. -What is the probability that exactly ten people out of fifteen people used an online travel website when they booked their hotel? Round to the nearest thousandth.

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

The normal model N(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 1.78. What is the weight of this egg in grams? Round to the nearest hundredth of a gram.

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

Explain the difference between a discrete random variable and a continuous random variable and give an example of each.

At a course in public speaking, the instructor always gives an opening speech that lasts between fifteen and eighteen minutes. The length of the speech can be modeled by a uniform distribution, that is, the speech is just as likely to last fifteen minutes as it is to last eighteen minutes. The probability density curve is shown below. What is the probability that the speech will last at least seventeen minutes? What is the probability that the speech will last between fifteen and sixteen minutes?