Question 1

The total area within any continuous probability distribution is equal to 1.00.

Accepted Answer

This statement is true and is a fundamental property of probability distributions. The probability of all possible outcomes within a distribution must add up to 1.00.

Question 2

The uniform probability distribution's standard deviation is proportional to the distribution's range.

Accepted Answer

This statement is true. The standard deviation of a uniform probability distribution is given by (range of distribution)/(sqrt(12)). Therefore, the standard deviation is directly proportional to the range.

Question 3

Some normal probability distributions are positively skewed.

Accepted Answer

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

Question 4

For a normal probability distribution,about 95 percent of the area under normal curve is within plus and minus two standard deviations of the mean and practically all (99.73 percent)of the area under the normal curve is within three standard deviations of the mean.

Accepted Answer

This statement is true and is a property of the normal distribution.

Question 5

The Empirical Rule of probability can be applied to the uniform probability distribution.

Accepted Answer

The Empirical Rule applies to normal distributions, not uniform distributions, as it describes the percentage of data within certain standard deviations from the mean in a bell-shaped curve.

Question 6

The uniform probability distribution is symmetric about the mean and median.

Accepted Answer

The uniform probability distribution is symmetrical, constant, and has a rectangular shape. Since the distribution is uniform, each value has an equal probability of occurring, and therefore the mean and median are located at the center of the distribution, making it symmetric around those values.

Question 7

For any continuous probability distribution,the probability,P(x),of any value of the random variable,X,can be computed.

Accepted Answer

In a continuous probability distribution, the probability of the random variable taking on any specific value is zero. Instead, probabilities are calculated over intervals.

Question 8

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

Accepted Answer

For a uniform distribution, the mean is equal to the average of the maximum and minimum values and the standard deviation is equal to the difference between the maximum and minimum values divided by the square root of 12. Therefore, knowing the maximum and minimum values allows us to compute both the mean and standard deviation.

Question 9

In a uniform probability distribution,P(x)is constant between the distribution's minimum and maximum values.

Accepted Answer

This is the definition of a uniform probability distribution.

Question 10

Some normal probability distributions have different arithmetic means and different standard deviations.

Accepted Answer

This is true. Different normal distributions can have different means and standard deviations, which determine the shape, center, and spread of the distribution.

Question 11

Areas within a continuous probability distribution represent probabilities.

Accepted Answer

Areas within a continuous probability distribution represent the probability of a random variable falling within that range of values. Therefore, the area under the curve must add up to 1.

Question 12

Some normal probability distributions have equal arithmetic means,but their standard deviations may be different.

Accepted Answer

This is true. Two different normal distributions can have the same mean but different standard deviations.

Question 13

The total area under the normal curve is 100%.

Accepted Answer

This is because the normal distribution is a probability distribution and must have a total probability of 1 or 100%.

Question 14

For a uniform probability distribution,the probability of any event is equal to 1/(b-a).

Accepted Answer

The answer of For a uniform probability distribution,the probability of...

Question 15

The uniform probability distribution is symmetric about the mode.

Accepted Answer

The uniform probability distribution is symmetric about its mean, not the mode. In a uniform distribution, all outcomes are equally likely, so there is no single mode.

Question 16

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

Accepted Answer

This statement is true. The normal probability distribution family includes all distributions that follow the normal curve shape, but with different means and standard deviations.

Question 17

The area under the normal curve within plus and minus one standard deviation of the mean is about 68.26%.

Accepted Answer

This statement is true. The area within plus and minus one standard deviation of the mean covers about 68.26% of the total area under the normal curve.

Question 18

Asymptotic means that the normal curve gets closer and closer to the X-axis but never actually touches it.

Accepted Answer

Asymptotic means that a curve or line approaches a particular point or line, but never touches it. In the case of a normal distribution, the curve will get closer and closer to the x-axis, but will never touch or cross it.

Question 19

The uniform probability distribution's shape is a rectangle.

Accepted Answer

The uniform probability distribution has equal probability over a specified interval, resulting in a rectangle shape.

Question 20

The total area within a continuous probability distribution is equal to 100.

Accepted Answer

The total area under a continuous probability distribution is equal to 1, representing the entire probability space.

Quiz 7: Continuous Probability Distributions