Deck 6: Continuous Probability Distributions

Question 1

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)Both the probability at a given value of x and the area under the curve at x are correct answers.
D)the height of the function at x

Answer 1

the height of the function at x

Question 2

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)zero

Answer 2

zero

Question 3

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

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

Answer 3

0.75

Question 4

If arrivals follow a Poisson probability distribution, the time between successive arrivals must follow

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

Question 5

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 6

Whenever the probability is proportional to the length of the interval in which the random variable can assume a value, the random variable is

A)uniformly distributed
B)normally distributed
C)exponentially distributed
D)Poisson distributed

Question 7

The mean, median, and mode have the same value for which of the following probability distributions?

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

Question 8

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

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

Question 9

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

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

Question 10

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

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

Question 11

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

A)normal function
B)uniform function
C)Both the normal function and the uniform function are correct.
D)probability density function

Question 12

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

A)can not 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 13

The form of the continuous uniform probability distribution is

A)triangular
B)rectangular
C)bell-shaped
D)a series of vertical lines

Question 14

The assembly time for a product is uniformly distributed between 6 to 10 minutes. 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 15

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 16

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 17

There is a lower limit but no upper limit for a random variable that follows the

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

Question 18

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

Question 19

The probability distribution that can be described by just one parameter is the

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

Question 20

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)Either a or b could be correct depending on the magnitude of the standard deviation.
D)None of the alternative answers is correct.

Question 21

Z is a standard normal random variable. The P(-1.5 $\le$ z $\le$ 1.09) equals

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

Question 22

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

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

Question 23

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 24

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)0.3333
B)0.1334
C)16
D)None of the alternative answers is correct.

Question 25

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 can not be negative
D)None of the alternative answers is correct.

Question 26

A normal probability distribution

A)is a continuous probability distribution
B)is a discrete probability distribution
C)can be either continuous or discrete
D)always has a standard deviation of 1

Question 27

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 28

Z is a standard normal random variable. The P(1.05 $\le$ z $\le$ 2.13) equals

A)0.8365
B)0.1303
C)0.4834
D)None of the alternative answers is correct.

Question 29

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 30

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 31

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

A)The graph of the curve is the shape of a rectangle
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 three standard deviations of its mean
D)The mean is equal to the median, which is also equal to the mode.

Question 32

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

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

Question 33

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 34

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 35

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 36

The mean of a standard normal probability distribution

A)is always equal to 1
B)can be any value as long as it is positive
C)can be any value
D)None of the alternative answers is correct.

Question 37

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

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

Question 38

For a standard 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 39

Z is a standard normal random variable. The P(1.20 $\le$ z $\le$ 1.85) equals

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

Question 40

Z is a standard normal random variable. The P(1.41 $\lt$ z $\lt$ 2.85) equals

A)0.4772
B)0.3413
C)0.8285
D)None of the alternative answers is correct.

Question 41

Given that z is a standard normal random variable, what is the value of z if the area to the right of z is 0.1112?

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

Question 42

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 43

Excel's NORM.INV function can be used to compute

A)cumulative probabilities for a standard normal z value
B)the standard normal z value given a cumulative probability
C)cumulative probabilities for a normally distributed x value
D)the normally distributed x value given a cumulative probability

Question 44

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 45

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 46

Z is a standard normal random variable. The P(z $\ge$ 2.11) equals

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

Question 47

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 48

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 49

Excel's NORM.S.DIST function can be used to compute

A)cumulative probabilities for a standard normal z value
B)the standard normal z value given a cumulative probability
C)cumulative probabilities for a normally distributed x value
D)the normally distributed x value given a cumulative probability

Question 50

Excel's NORM.S.INV function can be used to compute

A)cumulative probabilities for a standard normal z value
B)the standard normal z value given a cumulative probability
C)cumulative probabilities for a normally distributed x value
D)the normally distributed x value given a cumulative probability

Question 51

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 52

Excel's NORM.DIST function can be used to compute

A)cumulative probabilities for a standard normal z value
B)the standard normal z value given a cumulative probability
C)cumulative probabilities for a normally distributed x value
D)the normally distributed x value given a cumulative probability

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

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 55

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 56

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 57

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 58

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 59

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 60

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 61

Exhibit 6-1
Consider the continuous random variable x, which has a uniform distribution over the interval from 20 to 28.
Refer to Exhibit 6-1. The probability density function has what value in the interval between 20 and 28?

A)0
B)0.050
C)0.125
D)1.000

Question 62

Exhibit 6-1
Consider the continuous random variable x, which has a uniform distribution over the interval from 20 to 28.
Refer to Exhibit 6-1. The mean of x is

A)0.000
B)0.125
C)23
D)24

Question 63

Exhibit 6-2
The travel time for a college student traveling between her home and her college is uniformly distributed between 40 and 90 minutes.
Refer to Exhibit 6-2. The probability that her trip will take exactly 50 minutes is

A)zero
B)0.02
C)0.06
D)0.20

Question 64

Exhibit 6-1
Consider the continuous random variable x, which has a uniform distribution over the interval from 20 to 28.
Refer to Exhibit 6-1. The probability that x will take on a value between 21 and 25 is

A)0.125
B)0.250
C)0.500
D)1.000

Question 65

Exhibit 6-2
The travel time for a college student traveling between her home and her college is uniformly distributed between 40 and 90 minutes.
Refer to Exhibit 6-2. The probability that her trip will take longer than 60 minutes is

A)1.00
B)0.40
C)0.02
D)0.600

Question 66

Exhibit 6-3
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.
Refer to Exhibit 6-3. What percent of players weigh between 180 and 220 pounds?

A)34.13%
B)68.26%
C)0.3413%
D)None of the alternative answers is correct.

Question 67

Exhibit 6-1
Consider the continuous random variable x, which has a uniform distribution over the interval from 20 to 28.
Refer to Exhibit 6-1. The probability that x will take on a value of at least 26 is

A)0.000
B)0.125
C)0.250
D)1.000

Question 68

Excel's EXPON.DIST function can be used to compute

A)exponents
B)exponential probabilities
C)cumulative exponential probabilities
D)Both exponential probabilities and cumulative exponential probabilities are correct.

Question 69

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 70

Exhibit 6-4
The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000.
Refer to Exhibit 6-4. What is the probability that a randomly selected individual with an MBA degree will get a starting salary of at least $30,000?

A)0.4772
B)0.9772
C)0.0228
D)0.5000

Question 71

Exhibit 6-3
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.
Refer to Exhibit 6-3. What is the minimum weight of the middle 95% of the players?

A)196
B)151
C)249
D)None of the alternative answers is correct.

Question 72

Exhibit 6-2
The travel time for a college student traveling between her home and her college is uniformly distributed between 40 and 90 minutes.
Refer to Exhibit 6-2. The probability that she will finish her trip in 80 minutes or less is

A)0.02
B)0.8
C)0.2
D)1.00

Question 73

Exhibit 6-1
Consider the continuous random variable x, which has a uniform distribution over the interval from 20 to 28.
Refer to Exhibit 6-1. The variance of x is approximately

A)2.309
B)5.333
C)32
D)0.667

Question 74

Excel's EXPON.DIST function has how many inputs?

A)2
B)3
C)4
D)5

Question 75

Exhibit 6-3
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.
Refer to Exhibit 6-3. The probability of a player weighing less than 250 pounds is

A)0.4772
B)0.9772
C)0.0528
D)0.5000

Question 76

Exhibit 6-3
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.
Refer to Exhibit 6-3. The probability of a player weighing more than 241.25 pounds is

A)0.4505
B)0.0495
C)0.9505
D)0.9010

Question 77

Exhibit 6-2
The travel time for a college student traveling between her home and her college is uniformly distributed between 40 and 90 minutes.
Refer to Exhibit 6-2. What is the random variable in this experiment?

A)the uniform distribution
B)40 minutes
C)90 minutes
D)the travel time

Question 78

Exhibit 6-4
The starting salaries of individuals with an MBA degree are normally distributed with a mean of $40,000 and a standard deviation of $5,000.
Refer to Exhibit 6-4. What is the random variable in this experiment?

A)the starting salaries
B)the normal distribution
C)$40,000
D)$5,000

Question 79

When using Excel's EXPON.DIST function, one should choose TRUE for the third input if

A)a probability is desired
B)a cumulative probability is desired
C)the expected value is desired
D)the correct answer is desired

Question 80

Exhibit 6-3
The weight of football players is normally distributed with a mean of 200 pounds and a standard deviation of 25 pounds.
Refer to Exhibit 6-3. What is the random variable in this experiment?

A)the weight of football players
B)200 pounds
C)25 pounds
D)the normal distribution