Question 1

A nickel and a dime are tossed. If an event is defined as a single toss of both coins where at least one head appears, what is the complement of that event?

Accepted Answer

The answer of A nickel and a dime are tossed....

Question 2

Fast food restaurants pride themselves in being able to fill orders quickly. A study was done at a local fast food restaurant to determine how long it took customers to receive their order at the drive thru. It was discovered that The time it takes for orders to be filled is exponentially distributed with a mean of 1.5 minutes. What is the probability that it takes less than one minute to fill an order?
A)0.1813
B)0.4866
C)0.6321
D)0.7769

Accepted Answer

The answer of Fast food restaurants pride themselves in being...

Question 3

The newest model of smart car is supposed to get excellent gas mileage. A thorough study showed that gas mileage (measured in miles per gallon) is normally distributed with a mean of 75 miles per gallon and a standard deviation of 10 miles per gallon. What is the probability that, if driven normally, the car will get 100 miles per gallon or better? ​​
A)0.6%
B)2.5%
C)6%
D)25%

Accepted Answer

The answer of The newest model of smart car is...

Question 4

A nickel and a dime are tossed. How many possible outcomes are in this event?​

Accepted Answer

The answer of A nickel and a dime are tossed....

Question 5

Fast food restaurants pride themselves in being able to fill orders quickly. A study was done at a local fast food restaurant to determine how long it took customers to receive their order at the drive thru. It was discovered that the time it takes for orders to be filled is exponentially distributed with a mean of 1.5 minutes. What is the probability density function for the time it takes to fill an order? ??
A) $f ( x ) = \frac { 1 } { 5 } e ^ { - \frac { x } { 5 } }$
B)? $f ( x ) = \frac { 1 } { 3 } e ^ { - \frac { x } { 3 } }$
C)? $f ( x ) = \frac { 2 } { 3 } e ^ { - \frac { 2 } { 3 } x }$
D)None of the above answers are correct.

Accepted Answer

The probability density function for an exponentially distributed random variable with mean $\mu$ is $f(x) = \frac{1}{\mu} e^{-\frac{x}{\mu}}$. Given the mean is 1.5, the correct function is $f(x) = \frac{2}{3} e^{-\frac{2}{3}x}$.

Question 6

Consider a random experiment of rolling 2 dice. The sample space for rolling two dice is shown. Let S be the set of all ordered pairs listed in the figure. What is probability of rolling a sum larger than 10?

Accepted Answer

The answer of Consider a random experiment of rolling 2...

Question 7

A health conscious student faithfully wears a device that tracks his steps. Suppose that the distribution of the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. One day he took 15,000 steps. What was his percentile on that day? ​​
A)95%
B)97.7%
C)99.7%
D)100%

Accepted Answer

To find the percentile, we calculate the z-score: z = (X - μ) / σ = (15000 - 10000) / 1500 = 3. A z-score of 3 corresponds to the 99.7th percentile in a standard normal distribution.

Question 8

Consider a random experiment of rolling 2 dice. The sample space for rolling two dice is shown. Let S be the set of all ordered pairs listed in the figure. What is probability of rolling a 7?

Accepted Answer

The answer of Consider a random experiment of rolling 2...

Question 9

The center of a normal curve is
A)always equal to zero.
B)the mean of the distribution.
C)always a positive number.
D)equal to the standard deviation.

Accepted Answer

The center of a normal curve is always at the mean of the distribution. This is a defining characteristic of the normal distribution.

Question 10

The triangular distribution is a good model for____________ distributions. ​​
A)uniform
B)skewed
C)normal

Accepted Answer

The triangular distribution is a good model for skewed distributions. This is because it allows for a mode, which can be shifted to represent the direction of skewness. On the other hand, a uniform distribution has no mode and a normal distribution is symmetrical, so the triangular distribution is not a good model for these types of distributions.

Question 11

A nickel and a dime are tossed. We are interested only in the event that includes at least one head appears on a single toss of both coins. What are the possible outcomes?

Accepted Answer

The answer of A nickel and a dime are tossed....

Question 12

The newest model of smart car is supposed to get excellent gas mileage. A thorough study showed that gas mileage (measured in miles per gallon) is normally distributed with a mean of 75 miles per gallon and a standard deviation of 10 miles per gallon. What value represents the 50^th percentile of this distribution? A)75 B)85 C)95 D)105

Accepted Answer

The 50th percentile of a normally distributed variable corresponds to its mean, which is 75 miles per gallon in this case.

Question 13

A health conscious student faithfully wears a device that tracks his steps. Suppose that the distribution of the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. How many steps would he have to take to make the cut for the top 5% for his distribution? ​​
A)7,533
B)8,078
C)10,000
D)12,467

Accepted Answer

To find the number of steps needed to be in the top 5%, we need to find the z-score that corresponds to the 95th percentile. Using a standard normal distribution table or calculator, we find this z-score to be approximately 1.645.

We can use the formula:

z = (x - μ) / σ

Solving for x:

x = z * σ + μ

Substituting the values:

x = 1.645 * 1,500 + 10,000 = 12,467

Therefore, the student would need to take 12,467 steps to make the cut for the top 5%.

Question 14

Which of the following is not a characteristic of the normal probability distribution?
A)The mean, median, and the mode are equal.
B)The mean of the distribution can be negative, zero, or positive.
C)The distribution is symmetrical.
D)The standard deviation must be 1.

Accepted Answer

The standard deviation of a normal distribution can be any positive value and is not limited to being 1.

Question 15

A health conscious student faithfully wears a device that tracks his steps. Suppose that the distribution of the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. What percent of the time does he exceed 13,000 steps?
A)2.28%
B)5.0%
C)95%
D)97.72%

Accepted Answer

Using the properties of the normal distribution, a Z-score can be calculated for 13,000 steps: Z = (13,000 - 10,000) / 1,500 = 2. The probability of a Z-score greater than 2 is approximately 2.28%.

Question 16

James has two fair coins. When he flips them, what is the sample space?

Accepted Answer

The answer of James has two fair coins. When he...

Question 17

What is the mean of x, given the exponential probability function $$f ( x ) = \frac { 1 } { 20 } e ^ { \frac { x } { 20 } } \text { for } x \geq 0 \text { ? }$$
A)0.05
B)20
C)100
D)2,000

Accepted Answer

The mean of an exponential distribution with the probability density function $ f(x) = \frac{1}{\lambda} e^{-\frac{x}{\lambda}} $ is $\lambda$. Here, $\lambda = 20$, so the mean is 20.

Question 18

What is the total area under the normal distribution curve? ​​
A)It depends upon the mean and standard deviation
B)It must be calculated
C)1
D)100

Accepted Answer

The total area under the normal distribution curve is always equal to 1, regardless of the mean and standard deviation. This is because the normal distribution is a probability distribution, and the probabilities of all possible outcomes must add up to 1.

Question 19

Consider a random experiment of rolling 2 dice. The sample space for rolling two dice is shown. Let S be the set of all ordered pairs listed in the figure. What are the possible outcomes for the event of rolling a 7?

Accepted Answer

The answer of Consider a random experiment of rolling 2...

Question 20

In a normal​ distribution, which is​ greater, the mean or the​ median? ​​
A)Mean
B)Median
C)Neither (they are equal)
D)Cannot be determined with the information provided

Accepted Answer

In a normal distribution, the mean and the median are equal because the distribution is symmetric around the mean.

Quiz 5: Probability: an Introduction to Modeling Uncertainty

A nickel and a dime are tossed. If an event is defined as a single toss of both coins where at least one head appears, what is the complement of that event?

A nickel and a dime are tossed. How many possible outcomes are in this event?

Consider a random experiment of rolling 2 dice. The sample space for rolling two dice is shown. Let S be the set of all ordered pairs listed in the figure. What is probability of rolling a sum larger than 10?

A health conscious student faithfully wears a device that tracks his steps. Suppose that the distribution of the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. One day he took 15,000 steps. What was his percentile on that day?

Consider a random experiment of rolling 2 dice. The sample space for rolling two dice is shown. Let S be the set of all ordered pairs listed in the figure. What is probability of rolling a 7?

The center of a normal curve is

The triangular distribution is a good model for____________ distributions.

A nickel and a dime are tossed. We are interested only in the event that includes at least one head appears on a single toss of both coins. What are the possible outcomes?

Which of the following is not a characteristic of the normal probability distribution?

A health conscious student faithfully wears a device that tracks his steps. Suppose that the distribution of the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. What percent of the time does he exceed 13,000 steps?

James has two fair coins. When he flips them, what is the sample space?

What is the mean of x, given the exponential probability function $f ( x ) = \frac { 1 } { 20 } e ^ { \frac { x } { 20 } } \text { for } x \geq 0 \text { ? }$

What is the total area under the normal distribution curve?

Consider a random experiment of rolling 2 dice. The sample space for rolling two dice is shown. Let S be the set of all ordered pairs listed in the figure. What are the possible outcomes for the event of rolling a 7?

In a normal distribution, which is greater, the mean or the median?

Quiz 5: Probability: an Introduction to Modeling Uncertainty

A nickel and a dime are tossed. If an event is defined as a single toss of both coins where at least one head appears, what is the complement of that event?

A nickel and a dime are tossed. How many possible outcomes are in this event?​

Consider a random experiment of rolling 2 dice. The sample space for rolling two dice is shown. Let S be the set of all ordered pairs listed in the figure. What is probability of rolling a sum larger than 10?

A health conscious student faithfully wears a device that tracks his steps. Suppose that the distribution of the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. One day he took 15,000 steps. What was his percentile on that day? ​​

Consider a random experiment of rolling 2 dice. The sample space for rolling two dice is shown. Let S be the set of all ordered pairs listed in the figure. What is probability of rolling a 7?

The center of a normal curve is

The triangular distribution is a good model for____________ distributions. ​​

A nickel and a dime are tossed. We are interested only in the event that includes at least one head appears on a single toss of both coins. What are the possible outcomes?

Which of the following is not a characteristic of the normal probability distribution?

A health conscious student faithfully wears a device that tracks his steps. Suppose that the distribution of the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. What percent of the time does he exceed 13,000 steps?

James has two fair coins. When he flips them, what is the sample space?

What is the mean of x, given the exponential probability function f(x) =120ex20 for x≥0 ? f ( x ) = \frac { 1 } { 20 } e ^ { \frac { x } { 20 } } \text { for } x \geq 0 \text { ? }f(x) =201​e20x​ for x≥0 ?

What is the total area under the normal distribution curve? ​​

Consider a random experiment of rolling 2 dice. The sample space for rolling two dice is shown. Let S be the set of all ordered pairs listed in the figure. What are the possible outcomes for the event of rolling a 7?

In a normal​ distribution, which is​ greater, the mean or the​ median? ​​

A nickel and a dime are tossed. How many possible outcomes are in this event?

A health conscious student faithfully wears a device that tracks his steps. Suppose that the distribution of the number of steps he takes is normally distributed with a mean of 10,000 and a standard deviation of 1,500 steps. One day he took 15,000 steps. What was his percentile on that day?

The triangular distribution is a good model for____________ distributions.

What is the mean of x, given the exponential probability function $f ( x ) = \frac { 1 } { 20 } e ^ { \frac { x } { 20 } } \text { for } x \geq 0 \text { ? }$

What is the total area under the normal distribution curve?

In a normal distribution, which is greater, the mean or the median?