Deck 6: Continuous Probability Distributions

Question 1

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

A)more than, 1 since the normal distribution has an upper bound of infinity
B)3.09
C)1.96
D)0.5

Answer 1

0.5

Question 2

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

A)a probability density function
B)an ordinary normal curve
C)a standard normal distribution
D)none of these alternatives is correct

Answer 2

a standard normal distribution

Question 3

The standard deviation of a normal distribution

A)is always greater than zero
B)is always 1
C)can be any value
D)cannot be negative

Answer 3

cannot be negative

Question 4

The uniform, normal, and exponential distributions are

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

Question 5

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 6

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 7

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 8

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

Question 9

A normal probability distribution

A)can have any value of the mean
B)must have a mean of 0
C)must have a standard deviation of 0
D)must have a standard deviation of 1 and a mean of 0

Question 10

Which of the following is a characteristic of the 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 11

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

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

Question 12

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 13

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)almost zero

Question 14

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 15

The center of a normal curve is

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

Question 16

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

A)50% of the area under the normal curve
B)continuity correction factor
C)factor of conversion
D)all of the alternatives are correct answers

Question 17

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)any mean and any standard deviation

Question 18

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

A)is any number between zero and 1
B)is more than 1, since it is contineous
C)is a value larger than zero
D)the random variable can't have a value less than zero

Question 19

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 20

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 21

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 22

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 23

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 24

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 25

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 26

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 27

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 28

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

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

Question 29

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)None of these alternatives is correct.

Question 30

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 31

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 32

For a uniform probability density function,

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

Question 33

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

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

Question 34

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

A)0.0000
B)0.0001
C)0.001
D)0.729

Question 35

When a continuous probability distribution is used to approximate a discrete probability distribution, a value of 0.5 is

A)added and/or subtracted from the area
B)added and/or subtracted from the value of x
C)added to the area
D)subtracted from the area

Question 36

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 37

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 38

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 39

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 40

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 41

A standard normal distribution is a normal distribution

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

Question 42

Z is a standard normal random variable. What is the value of Z if the area to the right of Z is 0.1112?

A)0.3888
B)1.22
C)2.22
D)3.22

Question 43

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

A)zero
B)-0.5
C)0.5
D)one

Question 44

Given that Z is a standard normal random variable, what is the probability that -2.51 $\le$ Z F $\le$ -1.53?

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

Question 45

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 46

X is a normally distributed random variable with a mean of 5 and a variance of 4. The probability that X is greater than 10.52 is

A)0.0029
B)0.0838
C)0.4971
D)0.9971

Question 47

The random variable x is known to be uniformly distributed between 70 and 90. The probability of x having a value between 80 to 95 is

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

Question 48

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 49

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 50

Z is a standard normal random variable. The P (-1.20 Z 1.50) equals

A)0.0483
B)0.3849
C)0.4332
D)0.8181

Question 51

Given that Z is a standard normal random variable, what is the value of Z if the are to the left of Z is 0.0559?

A)0.4441
B)1.59
C)0.0000
D)1.50

Question 52

X is a normally distributed random variable with a mean of 8 and a standard deviation of 4. The probability that X is between 1.48 and 15.56 is

A)0.0222
B)0.4190
C)0.5222
D)0.9190

Question 53

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 54

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 55

Z is a standard normal random variable. The P (1.20 Z 1.85) equals

A)0.4678
B)0.3849
C)0.8527
D)0.0829

Question 56

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

A) 0.8942
B) 0.0558
C) 0.475
D) 0.4192

Question 57

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 58

X is a normally distributed random variable with a mean of 22 and a standard deviation of 5. The probability that X is less than 9.7 is

A)0.000
B)0.4931
C)0.0069
D)0.9931

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

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 61

Exhibit 6-1
The assembly time for a product is uniformly distributed between 6 to 10 minutes.
Refer to Exhibit 6-1. The probability of assembling the product between 7 to 9 minutes is

A)zero
B)0.50
C)0.20
D)1

Question 62

Given that Z is a standard normal random variable. What is the value of Z if the area to the left of Z is 0.9382?

A)1.8
B)1.54
C)2.1
D)1.77

Question 63

For a standard normal distribution, the probability of obtaining a z value between -2.4 to -2.0 is

A)0.4000
B)0.0146
C)0.0400
D)0.5000

Question 64

Exhibit 6-1
The assembly time for a product is uniformly distributed between 6 to 10 minutes.
Refer to Exhibit 6-1. The probability of assembling the product in less than 6 minutes is

A)zero
B)0.50
C)0.15
D)1

Question 65

Z is a standard normal random variable. The P(1.05 < Z < 2.13) equals

A)0.8365
B)0.1303
C)0.4834
D)0.3531

Question 66

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 67

Given that Z is a standard normal random variable, what is the value of Z if the area to the right of Z is 0.9834?

A)0.4834
B)-2.13
C)+2.13
D)zero

Question 68

Given that Z is a standard normal random variable, what is the value of Z if the area between -Z and Z is 0.901?

A)1.96
B)-1.96
C)0.4505
D) 1.65

Question 69

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 70

For a standard normal distribution, the probability of obtaining a z value between -1.9 to 1.7 is

A)0.9267
B)0.4267
C)1.4267
D)0.5000

Question 71

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

A) 1.16
B) 1.96
C) 2.0
D) 11.6

Question 72

Exhibit 6-1
The assembly time for a product is uniformly distributed between 6 to 10 minutes.
Refer to Exhibit 6-1. The probability density function has what value in the interval between 6 and 10?

A)0.25
B)4.00
C)5.00
D)zero

Question 73

Given that Z is a standard normal random variable. What is the value of Z if the area to the right of Z is 0.1401?

A)1.08
B)0.1401
C)2.16
D)-1.08

Question 74

Exhibit 6-1
The assembly time for a product is uniformly distributed between 6 to 10 minutes.
Refer to Exhibit 6-1. The probability of assembling the product in 7 minutes or more is

A)0.25
B)0.75
C)zero
D)1

Question 75

For a standard normal distribution, the probability of obtaining a z value of less than 1.6 is

A)0.1600
B)0.0160
C)0.0016
D)0.9452

Question 76

Use the normal approximation to the binomial distribution to answer this question. Fifteen 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)0.0683
B)0.0213
C)0.0021
D)0.1329

Question 77

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 78

Exhibit 6-1
The assembly time for a product is uniformly distributed between 6 to 10 minutes.
Refer to Exhibit 6-1. The expected assembly time (in minutes) is

A)16
B)2
C)8
D)4

Question 79

Z is a standard normal random variable. What is the value of Z if the area to the right of Z is 0.9803?

A)-2.06
B)0.4803
C)0.0997
D)3.06

Question 80

Given that Z is a standard normal random variable, what is the value of Z if the area to the left of Z is 0.119?

A)0.381
B)+1.18
C)-1.18
D)2.36