Deck 6: Continuous Probability Distributions

Question 1

The exponential probability density function produces a downward sloping curve that approaches the x axis as values of x gets larger.

Answer 1

True

Question 2

Approximately 99.7% of the values in a normal distribution will be within three standard deviations of the distribution mean.

Answer 2

True

Question 3

Approximately 95.5% of the values in a normal distribution will be within two standard deviations of the distribution mean.

Answer 3

True

Question 4

A random variable that has a normal distribution with a mean of zero and a standard deviation of one is said to have a standard normal probability distribution.

Question 5

For a continuous probability distribution, it is possible to talk about the probability of a random variable assuming a particular value, just like is done in a discrete probability distribution.

Question 6

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

Question 7

For a continuous probability distribution, the probability is represented by the area under the curve.

Question 8

One of the interesting properties of the exponential distribution is its lack of memory.

Question 9

In a continuous probability distribution, area, not height, represents probability.

Question 10

For a continuous uniform probability density function, the height of the function decreases as x increases.

Question 11

In the exponential distribution the expected value (mean) and variance are the same.

Question 12

A continuous random variable would be an appropriate way to describe the outcome of which of the following experiments?

A)the flavor of ice cream chosen by a randomly selected customer
B)the number of points a soccer team scores in its next game
C)the number of children born to a woman over the course of her lifetime
D)the commute time between a person's home and that person's workplace
E)the color of new car purchased by a customer

Question 13

The number of customers that enter a store during one day is an example of:

A)a continuous random variable
B)a discrete random variable
C)either a continuous or a discrete random variable, depending on the number of the customers
D)either a continuous or a discrete random variable, depending on the gender of the customers
E)none of the above

Question 14

In the graph of a continuous uniform probability function, the height of the function is different for various values of x.

Question 15

The probability of a continuous random variable taking on a value within some interval is the area under the graph of the probability density function.

Question 16

Approximately 68.3% of the values in a normal distribution will be within two standard deviations of the distribution mean.

Question 17

A continuous random variable may assume only fractional values in an interval or collection of intervals.

Question 18

Smaller values of the standard deviation result in a normal curve that is wider and flatter.

Question 19

For a continuous uniform probability distribution, the probability is proportional to the interval's width.

Question 20

When playing a round of golf, the distance of the drive off the second tee in feet is considered to be a continuous variable.

Question 21

Which of the following is NOT a property of the normal probability distribution?

A)symmetry
B)the total area under the curve is always equal to 1
C)99.7% of the time the random variable assumes a value within plus or minus one standard deviation of its mean
D)the mean is equal to the median, which is also equal to the mode.
E)none of the above

Question 22

Which of the following is NOT true of the normal probability distribution?

A)the graph of the curve is the shape of a bell curve
B)the total area under the curve is always equal to 1.
C)approximately 99.7% of the time the random variable assumes a value within plus or minus one standard deviation of its mean
D)the mean is equal to the median, which is also equal to the mode.
E)none of the above; all are characteristics

Question 23

Which of the following best describes the exponential distribution?

A)it produces probabilities for intervals of space, time, or distance between successive occurrences of a Poisson event
B)it is a discrete distribution that focuses on the number of events in a time period
C)it is similar to the normal distribution but focuses on distance
D)the mean and variance are the same
E)all of the above

Question 24

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 1.96
D)any mean and any standard deviation
E)none of the above

Question 25

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
E)none of the above

Question 26

Which of the following is NOT true of the normal probability distribution?

A)two parameters, the mean $\mu$ and the standard deviation $\sigma$ , determine the location and shape of the distribution
B)the total area under the curve is always equal to 1
C)approximately 68.3% of the values will be within two standard deviations of the distribution mean
D)the highest point is at the mean, which is also the median and the mode
E)the standard deviation determines the width of the curve

Question 27

To determine probability using the standard normal distribution:

A)first calculate a z-score for a given data value x
B)use the formula x = $\mu$ + z $\sigma$
C)first find the area associated with z
D)look in the standard normal table for the x value
E)none of the above

Question 28

Which of the following is NOT true of the normal probability distribution?

A)two parameters, the mean and the standard deviation, determine the location and shape of the distribution
B)the total area under the curve is always equal to 1
C)approximately 95.5% of the values will be within three standard deviations of the distribution mean
D)the highest point is at the mean, which is also the median and the mode
E)the normal curve is symmetric

Question 29

Which of the following best describes the memoryless nature of the exponential distribution?

A)it ignores any consideration of how long it has been since the last event occurred
B)it keeps track of everything that has occurred
C)it ignores any consideration of distance from the last event
D)it focuses only what has happened since the last two occurrences
E)a and b

Question 30

Which of the following is a property of the normal probability distribution?

A)the form, or shape, of the normal curve is often illustrated as a bell-shaped curve
B)two parameters, the mean and standard deviation determine the location and shape of the distribution
C)the standard deviation determines the width of the curve; larger values result in wider, flatter curves
D)approximately 99.7% of the values will be within three standard deviations of the distribution mean
E)all of the above

Question 31

The standard deviation of a normally distributed random variable:

A)cannot be greater than the variance of that variable
B)cannot be greater than the mean of that variable
C)cannot be less than zero
D)both a and c are true
E)none of the above

Question 32

Suppose that the probabilities for intervals of time between successive occurrences of an event are described by an exponential distribution.The standard deviation of this distribution:

A)is always less than the variance of the distribution
B)is always equal to the expected value of the distribution
C)is always greater than the variance of the distribution
D)is always equal to the variance of the distribution
E)a and b

Question 33

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 depending on the magnitude of the standard deviation
D)either a or b depending upon the magnitude of the mean
E)none of the above

Question 34

The distribution produces probabilities for intervals of space, time, or distance between successive occurrences of a Poisson event.

A)uniform
B)normal
C)exponential
D)Poisson
E)Chi-square

Question 35

A standard normal distribution is a normal distribution with a mean of and a standard deviation of .

A)1, 0
B)0, 1
C)any value, 1.96
D)any value, any value
E)none of the above

Question 36

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 a and b
D)the height of the function at x
E)none of the above

Question 37

A probability distribution is a continuous probability distribution where the probability that the random variable assumes a value in any interval of equal length is the same for each interval.

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

Question 38

For a random variable x, the probability density function f(x) represents the height of the function at x.

A)discrete
B)continuous
C)binomial
D)Poisson
E)none of the above

Question 39

The mean of a normally distributed random variable:

A)cannot be greater than the standard deviation of that variable
B)cannot be less than the standard deviation of that variable
C)cannot be negative
D)is always positive
E)none of the above

Question 40

Suppose that a random variable Y is uniformly distributed between 50 and 100.What might Y represent?

A)the number of donuts that will be sold tomorrow at a local bakery
B)snow depth in inches next Saturday at a nearby ski resort
C)the number of students who will attend next week's lecture on sustainability
D)the number of points scored by the winning team of the next women's basketball game at your college
E)the number of sandwiches sold at a local deli today

Question 41

Suppose that the time that your employees spend reading and answering e-mail each day varies between 1.5 and 3.5 hours and is uniformly distributed over this range of values.What is the probability that an employee spends more than two hours reading and answering e-mail?

A)20%
B)25%
C)50%
D)75%
E)90%

Question 42

The useful life (in years) of a shingled roof in Oregon has a uniform distribution described by the probability density function below.What proportion of roofs have a useful life of between 28.5 years and 29.5 years? 1/10 for values of x between 25 and 35
F(x) =
0 everywhere else

A).15
B).10
C).30
D).25
E).20

Question 43

Suppose that the high temperature on an August day in Death Valley varies between 98 and 118 degrees Fahrenheit and is uniformly distributed over this range of values.What is the probability that the high temperature will exceed 100 degrees on an August day?

A)10%
B)50%
C)90%
D)95%
E)100%

Question 44

Suppose that the high temperature on an August day in Death Valley varies between 98 and 118 degrees Fahrenheit and is uniformly distributed over this range of values.What is the expected value of the high temperature on an August day?

A)33.3 degrees Fahrenheit
B)100 degrees Fahrenheit
C)108 degrees Fahrenheit
D)125 degrees Fahrenheit
E)216 degrees Fahrenheit

Question 45

The useful life (in years) of a shingled roof in Oregon has a uniform distribution described by the probability density function below.What is the standard deviation of the useful life distribution? 1/10 for values of x between 25 and 35
F(x) =
0 everywhere else

A)2.886
B)3.446
C)2.467
D)4.890
E)5.118

Question 46

The search time for a particular search term on Google is defined by the probability density function below, where x = the random variable "time to produce a result in milliseconds".Determine the probability that the search will take no more than 253.5 milliseconds. 1/5 for values of x between 250 and 255
F(x) =
0 everywhere else

A).50
B).65
C).70
D).80
E).90

Question 47

For a normal distribution, find the area between the mean and a point 1.64 standard deviations to the left of the mean.

A).3554
B).4909
C).4881
D).4495
E).3749

Question 48

Random variable x has a uniform distribution defined by the probability density function below.Determine the probability that x has a value between 225 and 250. 1/100 for values of x between 200 and 300
F(x) =
0 elsewhere else

A).325
B).25
C).50
D).20
E).225

Question 49

The search time for a particular search term on Google is defined by the probability density function below, where x = the random variable "time to produce a result in milliseconds".Determine the mean (expected value) of x. 1/5 for values of x between 250 and 255
f(x) =
0 everywhere else

A)25.5
B)252.5
C)253.0
D)225
E)250.5

Question 50

Random variable x has a uniform distribution defined by the probability density function below.Determine the variance of x. 1/100 for values of x between 200 and 300
f(x) =
0 everywhere else

A)833.33
B)766.67
C)516.33
D)993.67
E)1033.33

Question 51

The useful life (in years) of a shingled roof in Oregon has a uniform distribution described by the probability density function below.40% of shingled roofs in Oregon have a useful life between 27 years and how many years. 1/10 for values of x between 25 and 35
F(x) =
0 everywhere else

A)32.5
B)34
C)33.2
D)31
E)30.6

Question 52

The search time for a particular search term on Google is defined by the probability density function below, where x = the random variable "time to produce a result in milliseconds".Determine the probability that the search will take between 251 and 251.5 milliseconds. 1/5 for values of x between 250 and 255
f(x) =
0 everywhere else

A).20
B).156
C).125
D).225
E).10

Question 53

Suppose that the time that your employees spend reading and answering e-mail each day varies between 1.5 and 3.5 hours and is uniformly distributed over this range of values.Determine the standard deviation of the "time spent reading and answering e-mail" random variable.

A)0.33 hours
B)0.58 hours
C)33%
D)58%
E)75%

Question 54

Random variable x has a uniform distribution defined by the probability density function below.Determine the mean (expected value) of x. 1/100 for values of x between 200 and 300
F(x) =
0 everywhere else

A)220
B)280
C)220.0
D)250
E)290

Question 55

The useful life (in years) of a shingled roof in Oregon has a uniform distribution described by the probability density function below.What proportion of roofs have a useful life greater than 29 years? 1/10 for values of x between 25 and 35
F(x) =
0 everywhere else

A).60
B).55
C).40
D).50
E).35

Question 56

The search time for a particular search term on Google is defined by the probability density function below, where x = random variable "time to produce a result in milliseconds".Determine the standard deviation of x. 1/5 for values of x between 250 and 255
f(x) =
0 everywhere else

A)2.083
B)3.001
C)1.673
D)2.298
E)1.443

Question 57

Random variable x has a uniform distribution defined by the probability density function below.Determine the standard deviation of the random variable. 1/100 for values of x between 200 and 300
F(x) =
0 everywhere else

A)32.45
B)16.38
C)22.81
D)36.52
E)28.87

Question 58

For a normal distribution, find the area between the mean and a point 2.33 standard deviations to the right of the mean.

A).4901
B).3980
C).4756
D).4985
E).4292

Question 59

For a normal distribution, find the area to the right of a value that is 1.96 standard deviations below the mean.

A).9162
B).3554
C).9750
D).8790
E).8997

Question 60

Random variable x has a uniform distribution defined by the probability density function below.Determine the probability that x has a value of at least 220. 1/100 for values of x between 200 and 300
F(x) =
0 everywhere else

A).65
B).80
C).75
D).60
E).85

Question 61

For a standard normal distribution, determine that probability that z is between -1.1 and +1.4; that is, find P(-1.1 < z < 1.4).

A).6549
B).7335
C).7835
D).8023
E).8772

Question 62

North Dakota Mining (NDM) describes its estimate of the amount of oil it will produce next year from its western North Dakota operations with a normal distribution.The distribution is centered on 5.2 million barrels and has a standard deviation of .7 million barrels.According to this distribution, how likely is it that NDM's production will be between 5.5 and 6.5 million barrels?

A).3577
B).3997
C).3022
D).3508
E).4049

Question 63

A study reported by the Michigan State campus newspaper stated that the average time MSU students spent studying last month was is 58.3 hours, with a standard deviation of 14 hours.If the study time distribution is normal, what percentage of students spent less than 60 hours studying?

A).6026
B).5948
C).6368
D).5478
E).5753

Question 64

For a standard normal distribution, find the area between z = -1.68 and z = +1.4.

A).8577
B).8971
C).8727
D).0987
E).1064

Question 65

A study reported by the Michigan State campus newspaper stated that the average time MSU students spent studying last month was is 58.3 hours, with a standard deviation of 14 hours.If the study time distribution is normal, what percentage of students spent between 40 and 80 hours studying?

A).8443
B).7486
C).8051
D).7224
E)..8962

Question 66

A study reported by the Michigan State campus newspaper stated that the average time MSU students spent studying last month was is 58.3 hours, with a standard deviation of 14 hours.Assume the study time distribution is normal.According to study results, about 20% of MSU students spent less than how many hours last month studying.

A)44.6
B)45.1
C)43.2
D)46.5
E)40.0

Question 67

JewelMist.com estimates the cost of relocating its headquarters to Los Gatos, CA with a normal distribution centered on $9.5 million and having a standard deviation of $1.1 million.According to this distribution, there's a 45% chance that the cost will be between $9.5 million and $ how many million.(Make $9.5 million the lower boundary for your interval.)

A)11.315
B)10.783
C)9.961
D)11.652
E)10.782

Question 68

For a standard normal distribution, find the area between z = +1.36 and z = + 2.22.

A).4162
B).0596
C).1406
D).3289
E).0737

Question 69

For a standard normal distribution, determine that probability that z is greater than or equal to 2.67; that is, find P(z > 2.6).

A).0478
B).0160
C).0038
D).1406
E).1331

Question 70

What proportion of values in a normal distribution will be in an interval that starts at 2.58 standard deviations to the left of (or below) the mean and ends at 1.96 standard deviations to the left of (or below) the mean?

A).0574
B).0662
C).0201
D).1021
E).0062

Question 71

What proportion of values in a normal distribution will be between the mean and a point 1.75 standard deviations to the right of (or above) the mean?

A).4599
B).5464
C).4013
D).3997
E).3761

Question 72

North Dakota Mining (NDM) describes its estimate of the amount of oil it will produce next year from its western North Dakota operations with a normal distribution.The distribution is centered on 5.2 million barrels and has a standard deviation of .7 million barrels.According to this distribution, how likely is it that NDM's production will be less than 4.5 million barrels?

A).1736
B).1587
C).2019
D).2794
E).2823

Question 73

North Dakota Mining (NDM) describes its estimate of the amount of oil it will produce next year from its western North Dakota operations with a normal distribution.The distribution is centered on 5.2 million barrels and has a standard deviation of .7 million barrels.According to this distribution, there is a .005 probability that NDM's production will be greater than how many millions of barrels?

A)6.4
B)7.0
C)6.1
D)7.5
E)6.8

Question 74

A study reported by the Michigan State campus newspaper stated that the average time MSU students spent studying last month was is 58.3 hours, with a standard deviation of 14 hours.If the study time distribution is normal, what percentage of students spent more than 70 hours studying?

A).3749
B).2454
C).2005
D).1772
E).2823

Question 75

For a standard normal distribution, determine that probability that z is between 0 and 1.48; that is, find P(0 < z < 1.48).

A).4265
B).4793
C).4850
D).4949
E).4306

Question 76

What proportion of values in a normal distribution will be in an interval that starts at 2.0 standard deviations to the left of (or below) the mean and extends to 1.0 standard deviation to the right of (or above) the mean?

A).7157
B).8365
C).8185
D).9162
E).8925

Question 77

For a standard normal distribution, determine that probability that z is between 2.2 and 2.55; that is, find P(2.2 < z < 2.55).

A).0085
B).0583
C).0116
D).0012
E).0487

Question 78

North Dakota Mining (NDM) describes its estimate of the amount of oil it will produce next year from its western North Dakota operations with a normal distribution.The distribution is centered on 5.2 million barrels and has a standard deviation of .7 million barrels.According to this distribution, how likely is it that NDM's production will be between 4.8 and 6.0 million barrels?

A).3944
B).4162
C).6406
D).5596
E).5886

Question 79

What proportion of values in a normal distribution will be above 2.33 standard deviations to the right of (or above) the mean?

A).0802
B).0126
C).0221
D).0099
E).0398

Question 80

For a standard normal distribution, find the area between z = -.67 and z = +.15.

A).4692
B).0239
C).9756
D).7328
E).7024