Question 1

A group of normal distributions can have equal arithmetic means but different standard deviations.

Accepted Answer

The arithmetic mean is a measure of central tendency that is not affected by the spread of the data, which is measured by the standard deviation. Therefore, it is possible for different normal distributions to have the same arithmetic mean but different standard deviations.

Question 2

The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the probability that a flight is less than 135 minutes?
A)1.00
B)0.50
C)0.25
D)0.00

Accepted Answer

Since the distribution is uniform, the probability is equal to the proportion of the distance between 120 and 135 minutes to the total distance between 120 and 150 minutes.
Therefore, P(flight < 135 mins) = (135 - 120) / (150 - 120) = 15 / 30 = 0.5.

Question 3

The mean of any uniform probability distribution is _________.
A)(b - a)/2
B)(a + b)/2
C) 
D)nπ

Accepted Answer

The mean of a uniform probability distribution is the average of the minimum and maximum values, which is (a+b)/2.

Question 4

For a uniformly distributed random variable, x, P(x) = 1/(b - a).

Accepted Answer

This is the formula for the probability density function of a uniformly distributed random variable.

Question 5

The standard deviation of any uniform probability distribution is ____________.
A)(b - a)/2
B)n(1 - π)
C) 
D)

Accepted Answer

The answer of The standard deviation of any uniform probability...

Question 6

The number of different standard normal distributions is unlimited.

Accepted Answer

There is only one standard normal distribution, characterized by a mean of 0 and a standard deviation of 1.

Question 7

Within plus and minus one standard deviation of the mean, the area under any normal curve is about 68%.

Accepted Answer

This statement is a basic property of the normal distribution, known as the empirical rule or the 68-95-99.7 rule. It states that about 68% of the data falls within one standard deviation of the mean, about 95% within two standard deviations, and about 99.7% within three standard deviations.

Question 8

The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the distribution's standard deviation?
A)8.66 minutes
B)75 minutes
C)135 minutes
D)270 minutes

Accepted Answer

The formula for the standard deviation of a uniform distribution is (b-a)/sqrt(12), where a is the minimum and b is the maximum. 
Therefore, the standard deviation in this case would be (150-120)/sqrt(12) which simplifies to 30/sqrt(12) or approximately 8.66 minutes.

Question 9

The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the distribution's mean?
A)120 minutes
B)150 minutes
C)135 minutes
D)270 minutes

Accepted Answer

The mean of a uniform distribution is simply the average of the minimum and maximum values, which in this case is (120+150)/2 = 135 minutes.

Question 10

The upper and lower limits of a uniform probability distribution are __________.
A)Positive and negative infinity
B)Plus and minus three standard deviations
C)0 and 1
D)The maximum and minimum values of the random variable

Accepted Answer

The upper and lower limits of a uniform probability distribution represent the maximum and minimum possible values of the random variable. Therefore, D is the best choice.

Question 11

The z-scores for X values greater than the mean are negative.

Accepted Answer

The z-score for X values greater than the mean will always be positive, not negative.

Question 12

The shape of any uniform probability distribution is ____________.
A)Negatively skewed
B)Positively skewed
C)Rectangular
D)Bell-shaped

Accepted Answer

A uniform probability distribution is one where all values between a certain range have an equal chance of occurring. Therefore, the shape of this distribution is rectangular.

Question 13

For any uniform probability distribution, the mean and standard deviation can be computed based on the maximum and minimum values of the random variable.

Accepted Answer

For a uniform probability distribution, the mean can be computed as the average of the maximum and minimum values, and the standard deviation can be computed as the difference between the maximum and minimum values divided by the square root of 12.

Question 14

The standard normal distribution is a special normal distribution with a mean of 0 and a standard deviation of 1.

Accepted Answer

The standard normal distribution is defined as a normal distribution with a mean of 0 and a standard deviation of 1, which makes it a special case of the normal distribution.

Question 15

Some normal probability distributions are positively skewed.

Accepted Answer

Normal probability distributions are symmetric, not skewed; they have a skewness of zero.

Question 16

The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the probability that a flight is between 125 and 140 minutes?
A)1.00
B)0.50
C)0.33
D)10.00

Accepted Answer

The uniform distribution is defined by its minimum and maximum values, in this case, 120 minutes (min) and 150 minutes (max), respectively. The probability of any specific range within this distribution can be calculated by taking the length of the interval of interest (in this case, 140 - 125 = 15 minutes) and dividing it by the total range of the distribution (150 - 120 = 30 minutes). Therefore, the probability of a flight being between 125 and 140 minutes is 15/30 = 0.50.

Question 17

When referring to the normal probability distribution, there is not just one; there is a "family" of normal probability distributions.

Accepted Answer

This is true because there is not just one standard normal distribution; rather, there are infinitely many normal distributions with different means and variances.

Question 18

For a uniformly distributed random variable, x, P(x) is constant.

Accepted Answer

A uniform distribution means that the probability of any value in the distribution is constant, meaning P(x) is constant for all values of x.

Question 19

The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the probability that a flight is more than 140 minutes?
A)1.00
B)0.5
C)0.333
D)0.00

Accepted Answer

Since the time to fly is uniformly distributed, we can find the probability of a flight being more than 140 minutes by finding the proportion of the entire range that is greater than 140 minutes.

The total range is 150-120=30 minutes. The time beyond 140 minutes is 150-140=10 minutes. Therefore, the probability of a flight being more than 140 minutes is 10/30 or 0.333.

Question 20

Non-stop Airlines determined that the mean number of passengers per flight is 152 with a standard deviation of 10 passengers. Practically all flights have between 142 and 162 passengers.

Accepted Answer

The answer of Non-stop Airlines determined that the mean number...

Quiz 7: Continuous Probability Distributions

A group of normal distributions can have equal arithmetic means but different standard deviations.

The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the probability that a flight is less than 135 minutes?

The mean of any uniform probability distribution is _________.

For a uniformly distributed random variable, x, P(x) = 1/(b - a).

The standard deviation of any uniform probability distribution is ____________.

The number of different standard normal distributions is unlimited.

Within plus and minus one standard deviation of the mean, the area under any normal curve is about 68%.

The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the distribution's standard deviation?

The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the distribution's mean?

The upper and lower limits of a uniform probability distribution are __________.