Question 1

For a normal distribution,the z value for an x value that is to the right of the mean is always:
A)equal to zero
B)negative
C)greater than 1
D)positive

Accepted Answer

For a normal distribution, any x value to the right of the mean will have a positive z value because it is above the mean.

Question 2

The probability that a continuous random variable x assumes a single value is always:
A)less than 1
B)greater than zero
C)equal to zero
D)between zero and 1

Accepted Answer

For a continuous random variable, the probability of it assuming any single, specific value is always zero because there are infinitely many possible values it can take within any interval.

Question 3

A continuous random variable is a random variable that can:
A)assume only a countable set of values
B)assume any value in one or more intervals
C)have no random sample
D)assume no continuous random frequency

Accepted Answer

A continuous random variable can assume any value in one or more intervals.

Question 4

The relative frequency density for a class is obtained by dividing the:
A)frequency of that class by the class width
B)relative frequency of that class by the total frequency
C)relative frequency of that class by the class width
D)frequency of that class by the relative frequency

Accepted Answer

The relative frequency density is calculated by dividing the relative frequency of a class by the class width. This helps in creating histograms where the area of the bar represents the relative frequency.

Question 5

For a continuous random variable x,the area under the probability distribution curve between any two points is always:
A)greater than 1
B)less than zero
C)equal to 1
D)in the range zero to 1

Accepted Answer

The area under the probability distribution curve between any two points for a continuous random variable represents the probability of the variable falling within that range, which is always between 0 and 1.

Question 6

For the standard normal distribution,the mean is:
A)1 and the standard deviation is zero
B)0.5 and the standard deviation is 0.5
C)zero and the standard deviation is 1
D)1 and the standard deviation is 1

Accepted Answer

The standard normal distribution is defined to have a mean of zero and a standard deviation of one.

Question 7

The total area under a normal distribution curve to the right of the mean is always:
A)equal to 1
B)equal to zero
C)equal to 0.5
D)greater than .5

Accepted Answer

The total area under a normal distribution curve is 1, and since the curve is symmetric about the mean, the area to the right of the mean is 0.5.

Question 8

For a normal distribution,the z value for the mean is always:
A)equal to zero
B)negative
C)equal to 1
D)positive

Accepted Answer

In a normal distribution, the z-score for the mean is always zero because it represents the number of standard deviations a data point is from the mean, and the mean is zero standard deviations from itself.

Question 9

For the standard normal distribution,the z value gives the distance between the mean and a point in terms of the:
A)mean
B)standard deviation
C)variance
D)center of the curve

Accepted Answer

The z value represents the number of standard deviations a data point is away from the mean.

Question 10

For a continuous random variable x,the probability that x assumes a value in an interval is:
A)in the range zero to 1
B)greater than 1
C)less than zero
D)greater than 2

Accepted Answer

The probability that a continuous random variable assumes a value in an interval is always between 0 and 1, inclusive.

Question 11

The parameters of the normal distribution are:
A) 
B) 
C) 
D)

Accepted Answer

The answer of The parameters of the normal distribution are:
A)...

Question 12

The total area under a normal distribution curve to the left of the mean is always:
A)equal to 1
B)equal to zero
C)equal to 0.5
D)greater than .5

Accepted Answer

The total area under a normal distribution curve is 1, and since the curve is symmetric about the mean, the area to the left of the mean is 0.5.

Question 13

For a continuous random variable x,the total probability of all (mutually exclusive)intervals within which x can assume a value is:
A)less than 1
B)greater than 1
C)equal to 1
D)between zero and 1

Accepted Answer

The total probability of all possible outcomes for a continuous random variable is always equal to 1, as it represents the entire sample space.

Question 14

Which of the following is not a characteristic of the normal distribution?
A)The total area under the curve is 1.0
B)The curve is symmetric about the mean
C)The value of the mean is always greater than the value of the standard deviation
D)The two tails of the curve extend indefinitely

Accepted Answer

The mean of a normal distribution can be less than, equal to, or greater than the standard deviation; there is no fixed relationship between the two.

Question 15

The tails of a normal distribution curve:
A)meet the horizontal axis at z = 3.0
B)never meet or cross the horizontal axis
C)cross the horizontal axis at z = 4.0
D)are nonsymmetric

Accepted Answer

The tails of a normal distribution curve never meet or cross the horizontal axis.

Question 16

For a continuous random variable x,the total area under the probability distribution curve of x is always:
A)less than 1
B)greater than 1
C)equal to 1
D)between zero and 1

Accepted Answer

The total area under the probability distribution curve of a continuous random variable is always equal to 1, as it represents the total probability of all possible outcomes.

Question 17

For the standard normal distribution,the area between z = 0 and z = 1.70,rounded to four decimal places,is:

Accepted Answer

The answer of For the standard normal distribution,the area between...

Question 18

For a normal distribution,the spread of the curve decreases and its height increases as:
A)the sample size decreases
B)the standard deviation decreases
C)the ratio of the mean and standard deviation increases
D)the mean increases

Accepted Answer

When the standard deviation decreases, the spread of the curve decreases, and the height of the curve increases, as the data points are closer to the mean.

Question 19

The normal probability distribution is applied to:
A)a discrete random variable
B)a continuous random variable
C)any random variable
D)a subjective random variable

Accepted Answer

The normal probability distribution is applied to a continuous random variable because it can take on any value within a given range.

Question 20

For a normal distribution,the z value for an x value that is to the left of the mean is always:
A)equal to zero
B)negative
C)less than 1
D)positive

Accepted Answer

In a normal distribution, the z value represents the number of standard deviations an x value is from the mean. If the x value is to the left of the mean, it is less than the mean, resulting in a negative z value.

Quiz 6: Continuous Random Variables and the Normal Distribution

For a normal distribution,the z value for an x value that is to the right of the mean is always:

The probability that a continuous random variable x assumes a single value is always:

A continuous random variable is a random variable that can:

The relative frequency density for a class is obtained by dividing the:

For a continuous random variable x,the area under the probability distribution curve between any two points is always:

For the standard normal distribution,the mean is:

The total area under a normal distribution curve to the right of the mean is always:

For a normal distribution,the z value for the mean is always:

For the standard normal distribution,the z value gives the distance between the mean and a point in terms of the:

For a continuous random variable x,the probability that x assumes a value in an interval is:

The parameters of the normal distribution are:

The total area under a normal distribution curve to the left of the mean is always:

For a continuous random variable x,the total probability of all (mutually exclusive) intervals within which x can assume a value is:

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

The tails of a normal distribution curve:

For a continuous random variable x,the total area under the probability distribution curve of x is always:

For the standard normal distribution,the area between z = 0 and z = 1.70,rounded to four decimal places,is:

For a normal distribution,the spread of the curve decreases and its height increases as:

The normal probability distribution is applied to:

For a normal distribution,the z value for an x value that is to the left of the mean is always: