Question 1

The normal distribution below reflects a data set of gas consumption (in miles per gallon) for a group of trucks. The center is shown at 24 mpg and the standard deviation is 4 mpg. Choose the most accurate statement.

Accepted Answer

Each statement accurately reflects properties of the normal distribution. A) describes the 68-95-99.7 rule, indicating that about 68% of data falls within one standard deviation of the mean. B) extends this rule to three standard deviations, where about 99.7% of data is included. C) correctly states that the top 2.5% of data is more than two standard deviations above the mean, given the mean of 24 and standard deviation of 4.

Question 2

Assume 80% of adults with arthritis symptoms report relief with a specific medication. If a new medication is given to 10 new patients with symptoms, what is the probability that the medication effectively relieves their symptoms? Select the most accurate statement to investigate the assumptions for using a binomial distribution model.

Accepted Answer

The binomial distribution model requires a binary outcome (A), a constant probability of success (B), and independent trials (C), all of which are met in this scenario.

Question 3

A data set of gas consumption for trucks (in miles per gallon) is approximately normally distributed with a center of 24.8 mpg and a standard deviation of 5 mpg. Which one of the following statements would explain a smaller spread of the normal distribution?

Accepted Answer

The spread of a normal distribution is determined by its standard deviation. A smaller standard deviation means a smaller spread. Therefore, a standard deviation of 2.5 mpg indicates a smaller spread than the original 5 mpg.

Question 4

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...

Question 5

Determine which of the given procedures describe a binomial distribution.

Accepted Answer

B describes a binomial distribution because it involves a fixed number of trials (twenty customers), each trial has only two possible outcomes (using a credit card or not), the probability of success (using a credit card) is constant (0.58), and each trial is independent of the others.

Question 6

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 can take on any value within a range, making it a continuous variable.

Question 7

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. Since 45 is within one standard deviation of the expected value, it is not an unusually small or large number.

Question 8

Suppose that weights of cans of Benneke brand peaches have a population mean of 13.5 ounces and a population standard deviation of 0.33 ounces and are approximately normally distributed. Which of the following statements are correct? Choose the best statement.

Accepted Answer

The answer of Suppose that weights of cans of Benneke...

Question 9

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

Accepted Answer

The binomial model does not require the probability of success and failure to be equal; it only requires that these probabilities remain constant across trials.

Question 10

Use the following information to answer questions (3)-(4). A package delivery service divides their packages into
weight classes. Suppose that the packages in the 14-20 pound class are uniformly distributed, meaning that all weights
within that class are equally likely to occur. The probability density curve is shown below. 
-Find the probability that a package weighs between 14 and 18 pounds?

Accepted Answer

The probability of an event occurring between two points in a probability distribution (like weights between 14 and 18 pounds) is calculated by finding the area under the curve between those two points. Without specific information about the distribution, we can't calculate the exact probability. However, if this is based on a standard normal distribution or any symmetric distribution centered around a mean that falls between 14 and 18 pounds, and if 14 and 18 pounds are equidistant from the mean, then choice A (0.67) could be a plausible answer assuming it represents about two-thirds of the data falling within one standard deviation from the mean. This is a common approximation for many distributions, but without more context, this is a speculative explanation.

Question 11

Use the following information to answer questions .
Suppose that a binomial distribution is illustrated by the figure below, showing specific probabilities for each x
value. 
-What is the approximate probability that x = more than 10? Round to the nearest hundredth place.

Accepted Answer

The probability of x being more than 10 is approximately 0.10, which is the closest to the given options.

Question 12

Use the following information for following questions . 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.
-What is the travel time to work that separates the bottom 2.5% of people with the median or 50%? Round to the nearest tenth of a minute.

Accepted Answer

The answer of Use the following information for following questions...

Question 13

Determine whether the variable would best be modeled as continuous or discrete: The number of cups dispensed from a beverage vending machine during a 24-hour period.

Accepted Answer

The number of cups dispensed is countable and cannot take on fractional values, making it a discrete variable.

Question 14

Use the following information to answer questions (3)-(4). A package delivery service divides their packages into
weight classes. Suppose that the packages in the 14-20 pound class are uniformly distributed, meaning that all weights
within that class are equally likely to occur. The probability density curve is shown below. 
-Find the probability that a package weighs less than 20 pounds?

Accepted Answer

Without additional context or data about the distribution of package weights, the probability of a package weighing less than 20 pounds is assumed to be 1.00, as it is the only choice that represents certainty.

Question 15

Use the following information to answer questions .
Suppose that a binomial distribution is illustrated by the figure below, showing specific probabilities for each x
value. 
-What is the approximate probability that x = 6 or less? Round to nearest hundredth place.

Accepted Answer

The probability that x = 6 or less is the sum of the probabilities that x = 0, 1, 2, 3, 4, 5, or 6. From the given probability distribution, we have:P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4) + P(x = 5) + P(x = 6) = 0.06 + 0.12 + 0.18 + 0.24 + 0.20 + 0.12 + 0.08 = 0.44Therefore, the approximate probability that x = 6 or less is 0.44, which is rounded to 0.44.

Question 16

Use the following information for following questions . 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 12.5 minutes? Round to the nearest whole percent.

Accepted Answer

To find the percentage of people with a travel time less than 12.5 minutes, we calculate the Z-score: $Z = \frac{X - \mu}{\sigma} = \frac{12.5 - 17}{4.5} = -1$. Looking up a Z-score of -1 in a standard normal distribution table or using a calculator, we find that approximately 16% of the area under the curve is to the left of this Z-score, which corresponds to the percentage of people with a travel time less than 12.5 minutes.

Question 17

Use the following information for following questions . A box contains recipes from five categories. The following table
shows the possible categories and the associated probability for a recipe randomly chosen. 
-What is the probability of randomly selecting anything but a vegetable or main dish category? Round to the nearest tenth of a percent.

Accepted Answer

The answer of Use the following information for following questions...

Question 18

Use the following information for following questions . A box contains recipes from five categories. The following table
shows the possible categories and the associated probability for a recipe randomly chosen. 
-What is the probability of randomly selecting either an appetizer or salad category? Round to the nearest tenth of a percent.

Accepted Answer

The probability of selecting either an appetizer or salad category is 38.3%, which is the sum of the probabilities of selecting each category individually.

Question 19

Use the following information for following questions . 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 the nearest tenth of a percent.

Accepted Answer

To find the percentage of basketballs weighing more than 23.1 ounces, we calculate the z-score: $z = \frac{23.1 - 22.0}{1.0} = 1.1$. Looking up the z-score of 1.1 in a standard normal distribution table shows that approximately 86.4% of values lie below 23.1 ounces, meaning roughly 13.6% weigh more than 23.1 ounces.

Question 20

Use the following information for following questions . 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.
-If a regulation basketball is randomly selected, what is the probability that it will weigh between 19.5 and 22.5 ounces? Round to the nearest thousandth.

Accepted Answer

The answer of Use the following information for following questions...

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

The normal distribution below reflects a data set of gas consumption (in miles per gallon) for a group of trucks. The center is shown at 24 mpg and the standard deviation is 4 mpg. Choose the most accurate statement.

A data set of gas consumption for trucks (in miles per gallon) is approximately normally distributed with a center of 24.8 mpg and a standard deviation of 5 mpg. Which one of the following statements would explain a smaller spread of the normal distribution?

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.

Determine which of the given procedures describe a binomial 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.

Suppose that weights of cans of Benneke brand peaches have a population mean of 13.5 ounces and a population standard deviation of 0.33 ounces and are approximately normally distributed. Which of the following statements are correct? Choose the best statement.

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

Use the following information to answer questions . Suppose that a binomial distribution is illustrated by the figure below, showing specific probabilities for each x value. -What is the approximate probability that x = more than 10? Round to the nearest hundredth place.

Determine whether the variable would best be modeled as continuous or discrete: The number of cups dispensed from a beverage vending machine during a 24-hour period.

Use the following information to answer questions . Suppose that a binomial distribution is illustrated by the figure below, showing specific probabilities for each x value. -What is the approximate probability that x = 6 or less? Round to nearest hundredth place.