Deck 6: Continuous Probability Distributions

Question 1

The z score for the standard normal distribution

A) is always equal to zero.
B) can never be negative.
C) can be either negative or positive.
D) is always equal to the mean.

Answer 1

can be either negative or positive.

Question 2

The center of a normal curve

A) is always equal to zero.
B) is the mean of the distribution.
C) cannot be negative.
D) is the standard deviation.

Answer 2

is the mean of the distribution.

Question 3

A normal distribution with a mean of 0 and a standard deviation of 1 is called

A) a probability density function.
B) uniform probability distribution.
C) a standard normal distribution.
D) exponential probability distribution.

Answer 3

a standard normal distribution.

Question 4

A value of 0.5 that is added to and/or subtracted from a value of x when the continuous normal distribution is used to approximate the discrete binomial distribution is called

A) probability density factor.
B) continuity correction factor.
C) factor of conversion.
D) continuity approximation factor.

Question 5

For the standard normal probability distribution, the area to the right of the mean is

A) 1.
B) 3.09.
C) 1.96.
D) 0.5.

Question 6

The uniform, normal, and exponential distributions

A) are all continuous probability distributions.
B) are all discrete probability distributions.
C) can be either continuous or discrete, depending on the data.
D) are all the same distributions.

Question 7

In a standard normal distribution, the

A) mean and the standard deviation are both 1.
B) mean is 0 and the standard deviation is 1.
C) mean is 1 and the standard deviation is 0.
D) mean and the standard deviation can have any value.

Question 8

For a continuous random variable x, the probability density function f(x) represents the

A) probability at a given value of x.
B) area under the curve at x.
C) area under the curve to the right of x.
D) height of the function at x.

Question 9

A normal probability distribution

A) can have mean of any numerical value.
B) needs to have a mean of 0.
C) has a standard deviation of 0.
D) must have a standard deviation of 1 and a mean of 0.

Question 10

For any continuous random variable, the probability that the random variable takes a value less than zero

A) is any number between zero and one.
B) is more than one, since it is continuous.
C) is a value larger than zero.
D) is zero.

Question 11

For a normal distribution, a positive value of z indicates that

A) all the observations must have had positive values.
B) the area corresponding to the z is either positive or negative.
C) the sample mean is smaller than the population mean.
D) the sample mean is larger than the population mean.

Question 12

In a standard normal distribution, the probability that Z is greater than zero is

A) 0.5.
B) equal to 1.
C) at least 0.5.
D) 1.96.

Question 13

The probability that a continuous random variable takes any specific value

A) is equal to zero.
B) is at least 0.5.
C) depends on the probability density function.
D) is very close to 1.0.

Question 14

For a continuous random variable x, the height of the function at x is

A) the probability at a given value of x.
B) 0.50, since it is the middle value.
C) a value less than zero.
D) named the probability density function f(x).

Question 15

For any continuous random variable, the probability that the random variable takes on exactly a specific value is

A) 1.00.
B) 0.50.
C) any value between 0 to 1.
D) 0.

Question 16

Which of the following is a characteristic of the standard normal probability distribution?

A) The mean, median, and the mode are not equal
B) The distribution is not symmetrical
C) The standard deviation must be 0
D) The standard deviation must be 1

Question 17

A negative value of z indicates that

A) the number of standard deviations of an observation is to the right of the mean.
B) the number of standard deviations of an observation is to the left of the mean.
C) a mistake has been made in computations, since z cannot be negative.
D) the data has a negative mean.

Question 18

A standard normal distribution is a normal distribution with

A) a mean of 1 and a standard deviation of 1.
B) a mean of 0 and a standard deviation of 0.
C) any mean and a standard deviation of 1.
D) a mean of 0 and standard deviation of 1.

Question 19

The uniform probability distribution is used with

A) a continuous random variable.
B) a discrete random variable.
C) a normally distributed random variable.
D) any random variable, as long as it is not nominal.

Question 20

The standard deviation of a normal distribution

A) is always 0.
B) is always 1.
C) can be any value.
D) cannot be negative.

Question 21

A continuous probability distribution that is useful in describing the time, or space, between occurrences of an event is a(n) _____ probability distribution.

A) normal
B) uniform
C) exponential
D) Poisson

Question 22

The mean of a standard normal probability distribution

A) is always equal to zero.
B) can be any value as long as it is positive.
C) can be any value.
D) is always greater than zero.

Question 23

For a normal distribution, a negative value of z indicates

A) a mistake has been made in computations, because z is always positive.
B) the area corresponding to the z is negative.
C) the z is to the left of the mean.
D) the z is to the right of the mean.

Question 24

In a standard normal distribution, the range of values of z is from

A) minus infinity to infinity.
B) -1 to 1.
C) 0 to 1.
D) -3.09 to 3.09.

Question 25

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

A) Symmetry
B) The total area under the curve is always equal to 1.
C) 99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean.
D) The mean is equal to the median, which is also equal to the mode.

Question 26

The function that defines the probability distribution of a continuous random variable is a

A) normal function.
B) uniform function.
C) either normal of uniform depending on the situation.
D) probability density function.

Question 27

The probability density function for a uniform distribution ranging between 2 and 6 is

A) 4.
B) undefined.
C) any positive value.
D) 0.25.

Question 28

For the standard normal probability distribution, the area to the left of the mean is

A) -0.5.
B) 0.5.
C) any value between 0 to 1.
D) 1.

Question 29

A continuous random variable is uniformly distributed between a and b. The probability density function between a and b is

A) zero.
B) (a - b).
C) (b - a).
D) 1/(b - a).

Question 30

The standard deviation of a standard normal distribution

A) is always equal to zero.
B) is always equal to one.
C) can be any positive value.
D) can be any value.

Question 31

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

Question 32

A normal probability distribution

A) is a continuous probability distribution.
B) is a discrete probability distribution.
C) can be either continuous or discrete.
D) must have a standard deviation of 1.

Question 33

A continuous random variable may assume

A) all values in an interval or collection of intervals.
B) only integer values in an interval or collection of intervals.
C) only fractional values in an interval or collection of intervals.
D) all the positive integer values in an interval.

Question 34

A uniform probability distribution is a continuous probability distribution where the probability that the random variable assumes a value in any interval of equal length is

A) different for each interval.
B) the same for each interval.
C) at least one.
D) zero.

Question 35

When a continuous probability distribution is used to approximate a discrete probability distribution, a value of 0.5 is added to and/or subtracted from the

A) area.
B) value of x.
C) value of z.
D) value of µ.

Question 36

Consider a binomial probability experiment with n = 3 and p = 0.1. Then, the probability of x = 0 is

A) 0.
B) 0.0001.
C) 0.001.
D) 0.729.

Question 37

Larger values of the standard deviation result in a normal curve that is

A) skewed to the right.
B) skewed to the left.
C) narrower and more peaked.
D) wider and flatter.

Question 38

The exponential probability distribution is used with

A) a discrete random variable.
B) a continuous random variable.
C) any probability distribution with an exponential term.
D) an approximation of the binomial probability distribution.

Question 39

If the mean of a normal distribution is negative,

A) the standard deviation must also be negative.
B) the variance must also be negative.
C) a mistake has been made in the computations, because the mean of a normal distribution cannot be negative.
D) none of these alternatives is correct.

Question 40

For a uniform probability density function, the height of the function

A) cannot be larger than one.
B) is the same for each value of x.
C) is different for various values of x.
D) decreases as x increases.

Question 41

The highest point of a normal curve occurs at

A) one standard deviation to the right of the mean.
B) two standard deviations to the right of the mean.
C) approximately three standard deviations to the right of the mean.
D) the mean.

Question 42

z is a standard normal random variable. The P (1.20 z 2.10) equals

A) 0.7618.
B) 0.2382.
C) 0.9028.
D) 0.0972.

Question 43

x is a normally distributed random variable with a mean of 12 and a standard deviation of 3. The probability that x equals 19.62 is

A) 0.000.
B) 0.0055.
C) 0.4945.
D) 0.9945.

Question 44

A standard normal distribution is a normal distribution with

A) a mean of 1 and a standard deviation of 0.
B) a mean of 0 and a standard deviation of 1.
C) any mean and a standard deviation of 1.
D) any mean and any standard deviation.

Question 45

x is a normally distributed random variable with a mean of 7 and a standard deviation of 2. The probability that x is between 6.48 and 7.56 is

A) 0.9524.
B) 0.0476.
C) 0.7872.
D) 0.2128.

Question 46

z is a standard normal random variable. The P(-1.96 z 1.4) equals

A) 0.9442.
B) 0.0558.
C) 0.8942.
D) 0.1058.

Question 47

Given that z is a standard normal random variable, what is the probability that -2.08 z 1.46?

A) 0.9091
B) 0.4812
C) 0.4279
D) 0.0533

Question 48

Given that z is a standard normal random variable, what is the probability that -2.51 z -1.53?

A) 0.4950
B) 0.4370
C) 0.0570
D) 0.9310

Question 49

Given that z is a standard normal random variable, what is the probability that z -2.12?

A) 0.4830
B) 0.9830
C) 0.017
D) 0.966

Question 50

x is a normally distributed random variable with a mean of 6 and a variance of 4. The probability that x is greater than 8.75 is

A) 0.9154.
B) 0.0846.
C) 0.0775.
D) 0.9225.

Question 51

Given that z is a standard normal random variable, what is the value of z if the area to the left of z is 0.2345?

A) -0.72
B) 0.28
C) 0.72
D) -0.28

Question 52

An exponential probability distribution

A) is a continuous distribution.
B) is a discrete distribution.
C) can be either continuous or discrete.
D) must be normally distributed.

Question 53

z is a standard normal random variable. The P (-2.20 z 2.20) equals

A) 0.9645.
B) 0.0355.
C) 0.0278.
D) 0.9722.

Question 54

z is a standard normal random variable. What is the value of z if the area to the right of z is 0.1213?

A) -1.17
B) 1.17
C) -0.17
D) 0.17

Question 55

z is a standard normal random variable. What is the value of z if the area between -z and z is 0.754?

A) 0.377
B) 0.123
C) 2.16
D) 1.16

Question 56

For a standard normal distribution, the probability of z 0 is

A) 0.
B) -0.5.
C) 0.5.
D) 1.

Question 57

The random variable x is known to be uniformly distributed between 70 and 100. The probability of x having a value between 80 to 95 is

A) 0.75.
B) 0.5.
C) 0.05.
D) 1.

Question 58

x is a normally distributed random variable with a mean of 24 and a standard deviation of 6. The probability that x is less than 11.5 is

A) 0.0186.
B) 0.9814.
C) 0.0076.
D) 0.9924.

Question 59

Given that z is a standard normal random variable, what is the value of z if the area to the right of z is 0.5?

A) 0.0000
B) 1.0000
C) 0.1915
D) 0.3413

Question 60

z is a standard normal random variable. The P (1.41 < z < 2.85) equals

A) 0.4978.
B) 0.4207.
C) 0.9185.
D) 0.0771.

Question 61

Given that z is a standard normal random variable, what is the value of z if the area between -z and z is 0.7243?

A) 3.09
B) 2.09
C) 0.09
D) 1.09

Question 62

The ages of students at a university are normally distributed with a mean of 21. What percentage of the student body is at least 21 years old?

A) It could be any value, depending on the magnitude of the standard deviation
B) 50%
C) 21%
D) 1.96%

Question 63

For a standard normal distribution, the probability of obtaining a z value between -1.6 to 1.8 is

A) 0.9093.
B) 0.0907.
C) 0.0189.
D) 0.9811.

Question 64

For a standard normal distribution, the probability of obtaining a z value of less than 1.65 is

A) 0.8977.
B) 0.0123.
C) 0.0495.
D) 0.9505.

Question 65

Use the normal approximation to the binomial distribution to answer this question. Eleven percent of all students at a large university are absent on Mondays. If a random sample of 12 names is called on a Monday, what is the probability that four students are absent?

A) 0.0285
B) 0.9935
C) 0.0065
D) 0.9715

Question 66

Given that z is a standard normal random variable, what is the value of z if the area to the right of z is 0.9634?

A) 1.79
B) -1.79
C) 0.79
D) -0.79

Question 67

The assembly time for a product is uniformly distributed between 2 to 10 minutes. What is the value of probability density function in the interval between 2 and 10?

A) 0.25
B) 0.125
C) 8.00
D) 0.00

Question 68

Given that z is a standard normal random variable, what is the value of z if the area to the right of z is 0.1801?

A) 0.91
B) -0.91
C) 0.09
D) -0.09

Question 69

Given that z is a standard normal random variable, what is the value of z if the area to the left of z is 0.0119?

A) -1.26
B) 1.26
C) -2.26
D) 2.26

Question 70

z is a standard normal random variable. What is the value of z if the area to the right of z is 0.7444?

A) -0.66
B) 0.66
C) -1.66
D) 1.66

Question 71

The assembly time for a product is uniformly distributed between 2to 10 minutes. The probability of assembling the product in 4minutes or more is

A) 0.25.
B) 0.75.
C) 0.
D) 1.

Question 72

The assembly time for a product is uniformly distributed between 2to 10 minutes. The probability of assembling the product between 7 to 9 minutes is

A) 0.
B) 0.50.
C) 0.2.
D) 0.25.

Question 73

The assembly time for a product is uniformly distributed between 2 to 10 minutes. The probability of assembling the product in less than 6 minutes is

A) 0.
B) 0.50.
C) 0.25.
D) 1.

Question 74

z is a standard normal random variable. The P(-1.5 < z < 1.09) equals

A) 0.4322.
B) 0.3621.
C) 0.7953.
D) 0.0711.

Question 75

Given that z is a standard normal random variable, what is the value of z if the area between -z and z is 0.9812?

A) 2.35
B) 2.07
C) 0.25
D) 1.96

Question 76

z is a standard normal random variable. The P(1.5 < z < 2.3) equals

A) 0.9439.
B) 0.0561.
C) 0.9225.
D) 0.0775.

Question 77

z is a standard normal random variable. The P(z ≥ 2.11) equals

A) 0.4821.
B) 0.9821.
C) 0.5.
D) 0.0174.

Question 78

The assembly time for a product is uniformly distributed between 6 to 10 minutes. The standard deviation of assembly time (in minutes) is approximately

A) 1.3333.
B) 1.1547.
C) 0.1111.
D) 0.5773.

Question 79

Given that z is a standard normal random variable, what is the value of z if the area to the left of z is 0.9582?

A) -1.7
B) 1.7
C) 0.7
D) -0.7

Question 80

For a standard normal distribution, the probability of obtaining a z value between -1.4 to -0.35 is

A) 0.7176.
B) 0.2824.
C) 0.5561.
D) 0.4439.