Question 1

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 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 the bottom 8% of people with the shortest travel times and the upper 92%? Round to the nearest tenth of a minute.

Accepted Answer

To find the travel time that separates the bottom 8%, we need to find the z-score that corresponds to the 8th percentile of a standard normal distribution, which is approximately -1.41. Using the formula: X = μ + Zσ, where μ = 17 and σ = 4.5, we get X = 17 + (-1.41)(4.5) ≈ 10.7 minutes.

Question 2

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.

Accepted Answer

To find the travel time that separates the top 12% from the lower 88%, we need to find the z-score that corresponds to the 88th percentile of a standard normal distribution. This z-score is approximately 1.175. Using the formula: X = μ + zσ, where μ = 17 and σ = 4.5, we calculate X = 17 + (1.175)(4.5) ≈ 22.3 minutes.

Question 3

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 the probability that a person between the ages of 19 and 24 buys at least one tabloid magazine per week is 0.115. If 500 randomly selected people between the ages of 19 and 24 were asked "Do you buy at least one tabloid magazine per week?", would you be surprised if 45 or more said yes to this question? Why?

Accepted Answer

The expected number of people who buy at least one tabloid magazine per week is 500 * 0.115 = 57.5. The standard deviation can be calculated using the formula for a binomial distribution: sqrt(n * p * (1-p)) = sqrt(500 * 0.115 * 0.885) ≈ 7.1. The range of usual values is approximately 57.5 ± 2*7.1, which is about 43.3 to 71.7. Since 45 is within this range, it would not be surprising.

Question 4

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?

Accepted Answer

The answer of At a course in public speaking, the...

Question 5

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 three of your friends each draws a chip (with replacement), what is the probability that at least one of your group of four will win the valuable prize? Round to the nearest thousandth.

Accepted Answer

The probability that none of the four people will win the prize is (3/5)^4 = 0.130. Therefore, the probability that at least one person will win the prize is 1 - 0.130 = 0.870.

Question 6

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.

Accepted Answer

The answer of The normal model N(58, 21)describes the distribution...

Question 7

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?

Accepted Answer

For a table to represent a probability distribution, the sum of all probabilities must equal 1. Without the actual probabilities provided, we cannot determine if they sum to 1, so the table cannot be confirmed as a probability distribution.

Question 8

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.

Accepted Answer

The temperature of a cup of coffee dispensed from a beverage vending machine can take on any value within a certain range, so it is best modeled as a continuous variable.

Question 9

Determine which of the given procedures describe a binomial distribution.

Accepted Answer

A binomial distribution describes the number of successes in a fixed number of independent Bernoulli trials, each with the same probability of success. In choice A, there is a fixed number of trials (20 customers), each customer has the same probability of using a credit card (0.58), and the outcome for each customer is independent.

Question 10

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.

Accepted Answer

This is a binomial probability problem where n = 15, k = 10, and p = 0.68. The probability is calculated using the binomial probability formula: P(X = k) = C(n, k) * p^k * (1-p)^(n-k). Plugging in the values, the probability is approximately 0.213.

Question 11

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.
-Out of ten randomly selected people, how many would you expect to use an online travel website to book their hotel, give or take how many? Round to the nearest whole person.

Accepted Answer

The answer of Use the following information to answer the...

Question 12

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?

Accepted Answer

The z-score for a basketball that weighs 23.75 ounces is (23.75 - 22.0) / 1.0 = 1.75. The area under the normal curve to the right of z = 1.75 is 0.0401, which means that it would be unusual to randomly select a regulation basketball and find that it weighs 23.75 ounces.

Question 13

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 at least fourteen out of fifteen people used an online travel website when they booked their hotel? Round to the nearest thousandth.

Accepted Answer

The probability of at least 14 out of 15 people using an online travel website is the complement of the probability of 13 or fewer people using an online travel website. The probability of 13 or fewer people using an online travel website is the sum of the probabilities of 0, 1, 2, ..., 13 people using an online travel website. This can be calculated using the binomial distribution with n = 15 and p = 0.68. The probability of 13 or fewer people using an online travel website is 0.022. Therefore, the probability of at least 14 out of 15 people using an online travel website is 1 - 0.022 = 0.978.

Question 14

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

Accepted Answer

The number of tomatoes harvested is a countable quantity, making it a discrete variable.

Question 15

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.

Accepted Answer

The probability of not drawing a marked chip in one draw is 3/5. The probability that none of the three people draw a marked chip is (3/5)^3 = 27/125 = 0.216. Therefore, the probability that at least one person draws a marked chip is 1 - 0.216 = 0.784.

Question 16

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.
-Which of these statements is asking for a measurement (i. e. is an inverse normal question)?

Accepted Answer

The question asks for a measurement, which is an inverse normal question.

Question 17

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 less than 15.5 minutes? Round to the nearest whole percent.

Accepted Answer

To find the percentage of people with a travel time less than 15.5 minutes, calculate the z-score: z = (15.5 - 17) / 4.5 = -0.33. Using a standard normal distribution table, a z-score of -0.33 corresponds to approximately 37%.

Question 18

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.

Accepted Answer

The answer of The normal model N(58, 21)describes the distribution...

Question 19

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

Accepted Answer

The outcome in a binomial model is typically binary (success/failure), not necessarily a discrete numerical variable.

Question 20

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.
-Which of these statements is asking for a probability?

Accepted Answer

Statement A is asking for the probability of travel times falling between thirteen and fifteen minutes, which is a typical probability question.

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

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.

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?

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.

Determine which of the given procedures describe a binomial distribution.

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.

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