Question 1

A normal distribution is symmetric; therefore the probability of being below the mean is 0.50 and the probability of being above the mean is 0.50.

Accepted Answer

This is correct. Due to the symmetric nature of the normal distribution, exactly half of the distribution falls below the mean and half falls above the mean. Therefore, the probability of being below the mean is 0.50 and the probability of being above the mean is also 0.50.

Question 2

Electronics Test
The time it takes a student to finish a electronics test has a uniform distribution between 50 and 70 minutes.
-{Electronics Test Narrative} What is the mean amount of time it takes a student to finish the test?

Accepted Answer

The answer of Electronics Test
The time it takes a student...

Question 3

Subway Waiting Time
At a subway station the waiting time for a subway is found to be uniformly distributed between 1 and 5 minutes.
-{Subway Waiting Time Narrative} What is the probability of waiting no more than 3 minutes?

Accepted Answer

The answer of Subway Waiting Time
At a subway station the...

Question 4

The probability that a standard normal random variable Z is less than -3.5 is approximately 0.

Accepted Answer

Since the standard normal distribution is continuous and symmetrical, the probability of Z being less than any specific value is always strictly between 0 and 1. Hence, the probability that Z is less than F1F1F1S1−F1F1F103.5 is not exactly 0, but it is extremely close to 0 and is commonly approximated as such. Therefore, the statement is true and the answer is A.

Question 5

Subway Waiting Time
At a subway station the waiting time for a subway is found to be uniformly distributed between 1 and 5 minutes.
-{Subway Waiting Time Narrative} What is the median waiting time for this subway?

Accepted Answer

The answer of Subway Waiting Time
At a subway station the...

Question 6

A random variable X has a normal distribution with mean 132 and variance 36.If x = 120, its corresponding value of Z is 2.0.

Accepted Answer

We can use the formula:

Z = (X - μ) / σ

where Z is the standard normal variable, X is the value of the normal variable, μ is the mean, and σ is the standard deviation (which is the square root of the variance).

Substituting the given values, we have:

2 = (120 - 132) / σ

Solving for σ, we get:

σ = -12 / 2 = -6

This is not possible, as the standard deviation cannot be negative. Therefore, the statement is false.

Question 7

The 10th percentile of a Z distribution has 10% of the Z-values lying above it.

Accepted Answer

The 10th percentile of a Z distribution has 10% of the Z-values lying below it, not above.

Question 8

In the standard normal distribution, z_0.05 = 1.645 means that 5% of all values of z are below 1.645 and 95% are above it.

Accepted Answer

In the standard normal distribution, z = 1.645 means that approximately 95% of all values of z are below 1.645 and approximately 5% are above it.

Question 9

If your golf score is 3 standard deviations below the mean, its corresponding value on the Z distribution is -3.

Accepted Answer

This statement is true. If your golf score is 3 standard deviations below the mean, it means that it is a very low score and it is an outlier in the distribution. The corresponding value on the standard normal distribution, also known as the Z distribution, is -3.

Question 10

Subway Waiting Time
At a subway station the waiting time for a subway is found to be uniformly distributed between 1 and 5 minutes.
-{Subway Waiting Time Narrative} What is the probability density function for this uniform distribution?

Accepted Answer

The answer of Subway Waiting Time
At a subway station the...

Question 11

If the value of Z is z = 99, that means you are at the 99th percentile on the Z distribution.

Accepted Answer

The value of Z (z-score) indicates how many standard deviations an element is from the mean, not the percentile rank in the distribution.

Question 12

A random variable X is standardized by subtracting the mean and dividing by the variance.

Accepted Answer

A random variable is standardized by subtracting the mean and dividing by the standard deviation, not the variance.

Question 13

Electronics Test
The time it takes a student to finish a electronics test has a uniform distribution between 50 and 70 minutes.
-{Electronics Test Narrative} Find the probability that a student will take exactly one hour to finish the test.

Accepted Answer

The answer of Electronics Test
The time it takes a student...

Question 14

Electronics Test
The time it takes a student to finish a electronics test has a uniform distribution between 50 and 70 minutes.
-{Electronics Test Narrative} What is the median amount of time it takes a student to finish the test?

Accepted Answer

The answer of Electronics Test
The time it takes a student...

Question 15

If we standardize the normal curve, we express the original X values in terms of their number of standard deviations away from the mean.

Accepted Answer

Standardizing the normal curve involves converting the X values to Z scores, which represent the number of standard deviations the original value is from the mean.

Question 16

A national standardized testing company can tell you your relative standing on an exam without divulging the mean or the standard deviation of the exam scores.

Accepted Answer

This is true, as the relative standing of an individual can be calculated based on their score in comparison to the rest of the test takers without revealing the mean or standard deviation.

Question 17

Subway Waiting Time
At a subway station the waiting time for a subway is found to be uniformly distributed between 1 and 5 minutes.
-{Subway Waiting Time Narrative} What is the probability that the subway arrives in the first minute and a half?

Accepted Answer

The answer of Subway Waiting Time
At a subway station the...

Question 18

Given that Z is a standard normal random variable, a negative value of Z indicates that the standard deviation of Z is negative.

Accepted Answer

A standard normal random variable Z cannot have a negative standard deviation, as standard deviation is always non-negative. A negative Z value simply indicates that the observed value is below the mean of the distribution.

Question 19

A random variable X has a normal distribution with a mean of 250 and a standard deviation of 50.Given that X = 175, its corresponding value of Z is -1.50.

Accepted Answer

The answer of A random variable X has a normal...

Question 20

Electronics Test
The time it takes a student to finish a electronics test has a uniform distribution between 50 and 70 minutes.
-{Electronics Test Narrative} Find the probability that a student will take no less than 55 minutes to finish the test.

Accepted Answer

The answer of Electronics Test
The time it takes a student...

Quiz 8: Continuous Probability Distributions

A normal distribution is symmetric; therefore the probability of being below the mean is 0.50 and the probability of being above the mean is 0.50.

Electronics Test The time it takes a student to finish a electronics test has a uniform distribution between 50 and 70 minutes. -{Electronics Test Narrative} What is the mean amount of time it takes a student to finish the test?

Subway Waiting Time At a subway station the waiting time for a subway is found to be uniformly distributed between 1 and 5 minutes. -{Subway Waiting Time Narrative} What is the probability of waiting no more than 3 minutes?

The probability that a standard normal random variable Z is less than -3.5 is approximately 0.

Subway Waiting Time At a subway station the waiting time for a subway is found to be uniformly distributed between 1 and 5 minutes. -{Subway Waiting Time Narrative} What is the median waiting time for this subway?

A random variable X has a normal distribution with mean 132 and variance 36.If x = 120, its corresponding value of Z is 2.0.

The 10th percentile of a Z distribution has 10% of the Z-values lying above it.

In the standard normal distribution, z0.05 = 1.645 means that 5% of all values of z are below 1.645 and 95% are above it.

If your golf score is 3 standard deviations below the mean, its corresponding value on the Z distribution is -3.

Subway Waiting Time At a subway station the waiting time for a subway is found to be uniformly distributed between 1 and 5 minutes. -{Subway Waiting Time Narrative} What is the probability density function for this uniform distribution?

If the value of Z is z = 99, that means you are at the 99th percentile on the Z distribution.

A random variable X is standardized by subtracting the mean and dividing by the variance.

Electronics Test The time it takes a student to finish a electronics test has a uniform distribution between 50 and 70 minutes. -{Electronics Test Narrative} Find the probability that a student will take exactly one hour to finish the test.

Electronics Test The time it takes a student to finish a electronics test has a uniform distribution between 50 and 70 minutes. -{Electronics Test Narrative} What is the median amount of time it takes a student to finish the test?

If we standardize the normal curve, we express the original X values in terms of their number of standard deviations away from the mean.

A national standardized testing company can tell you your relative standing on an exam without divulging the mean or the standard deviation of the exam scores.

Subway Waiting Time At a subway station the waiting time for a subway is found to be uniformly distributed between 1 and 5 minutes. -{Subway Waiting Time Narrative} What is the probability that the subway arrives in the first minute and a half?

Given that Z is a standard normal random variable, a negative value of Z indicates that the standard deviation of Z is negative.

A random variable X has a normal distribution with a mean of 250 and a standard deviation of 50.Given that X = 175, its corresponding value of Z is -1.50.

Electronics Test The time it takes a student to finish a electronics test has a uniform distribution between 50 and 70 minutes. -{Electronics Test Narrative} Find the probability that a student will take no less than 55 minutes to finish the test.

In the standard normal distribution, z_0.05 = 1.645 means that 5% of all values of z are below 1.645 and 95% are above it.