Deck 5: Continuous Random Variables and Probability Distributions

Question 1

We can convert any normal distribution to a distribution with a mean 0 and a variance 1.What is the distribution called?

A)Poisson distribution
B)standard normal distribution
C)hypergeometric distribution
D)marginal distribution

Answer 1

standard normal distribution

Question 2

When the distribution of a continuous random variable follows a uniform probability distribution and does not exceed a specific given value,its cumulative distribution function is graphed as a:

A)bell-shaped curve.
B)polygon.
C)rectangle.
D)straight line.

Answer 2

straight line.

Question 3

Let the random variable Z follow a standard normal distribution.Find the value k,such that P(Z > k)= 0.39.

A)0.28
B)1.23
C)-1.23
D)-0.28

Answer 3

0.28

Question 4

In computing probabilities for proportion or percentage intervals,we use a direct extension of the normal distribution approximation for the:

A)Poisson distribution.
B)hypergeometric distribution.
C)binomial distribution.
D)uniform distribution.

Question 5

Suppose that 19% of all sales are for amounts greater than $1,000.In a random sample of 30 invoices,what is the probability that more than six of the invoices are for over $1,000? Use the binomial approximation for the normal distribution.

A)0.4443
B)0.9440
C)0.5557
D)0.0560

Question 6

Let the random variable Z follow a standard normal distribution.Find P(0 < Z < 0.57).

A)0.2843
B)0.7843
C)0.2157
D)0.7157

Question 7

A function of continuous random variables which allows for graphical interpretations of their probability structure is called the:

A)cumulative distribution function.
B)probability density function.
C)uniform distribution.
D)expected value.

Question 8

The shape of the uniform probability distribution is:

A)negatively skewed.
B)positively skewed.
C)bell-shaped.
D)rectangular.

Question 9

The area under the probability density function for the uniform distribution is between:

A)-∞ and +∞.
B)0 and 1.
C)± three standard deviations from the mean of the distribution.
D)the maximum and minimum values of the random variable.

Question 10

Sales,investment,consumption,costs,and revenues are economic and business measures which can be represented by:

A)discrete variable.
B)fixed variables.
C)continuous random variables.
D)coefficients.

Question 11

Because measurements of random variables are rounded to some value,mathematical theory leads us to conclude that in reality,random variables for all applied problems are:

A)linear.
B)discrete.
C)coefficients.
D)medians.

Question 12

________ is the continuous probability distribution used most often for economics and business applications.

A)Normal probability distribution
B)Uniform distribution
C)Exponential distribution
D)Incremental distribution

Question 13

In a random experiment which leads to an outcome that can be represented by a continuous random variable,the average of the values taken as the number of replications becomes infinitely large is called the:

A)mode.
B)median.
C)expected value.
D)hypergeometric distribution.

Question 14

To obtain the probability that a continuous random variable falls in a specified range,we find the difference between the cumulative probabilities at the lower and upper end of the:

A)range.
B)median.
C)mode.
D)mean.

Question 15

The continuous random variable X is uniformly distributed over the interval [a,b].The mean of the probability distribution of X is:

A)(a + b)/ 2
B)n - ab
C)(b - a)/ 2
D)(a + b)/ n

Question 16

The shape of the normal probability density function is a symmetric bell-shaped curve centered on the:

A)variance.
B)standard deviation.
C)coefficient.
D)mean.

Question 17

To approximate a discrete distribution that has many different outcomes useful in most applied business and economic problems,we are,in fact,using the:

A)Poisson distribution.
B)normal distribution.
C)Hypergeometric distribution.
D)marginal distribution.

Question 18

Let the random variable Z follow a standard normal distribution.Find P(-2.21 < Z < 0).

A)0.9864
B)0.4864
C)0.0136
D)0.5136

Question 19

Because the probability of any specific value is 0 for a continuous random variable,the expected values for continuous random variables are computed using:

A)Bayes' Theorem.
B)an empirical formula.
C)a Venn diagram.
D)integral calculus.

Question 20

The function that may be used to find the probability that the random variable falls within a specific range is called the:

A)expected value.
B)uniform distribution.
C)probability density function.
D)linear function.

Question 21

One normal distribution has a mean of 5 and a standard deviation of 2.A second normal distribution has a mean of 6 and a standard deviation of 1.Which of the following statements is true?

A)The width of the first distribution is wider than the second distribution.
B)The central location of the first distribution is higher than the second distribution.
C)The dispersions of both distributions are the same.
D)The locations of both distributions are the same.

Question 22

What does the uniform and normal probability distribution have in common?

A)Both have the same standard deviation.
B)The mean,median,and mode are equal for each.
C)About 68% of the observations are within one standard deviation of the mean.
D)The uniform distribution uses discrete data;the normal distribution is based on continuous data.

Question 23

Let the random variable Z follow a standard normal distribution.Find P(-1.33 < Z < 0.78).

A)0.6905
B)0.2823
C)0.2177
D)0.3095

Question 24

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
You have recently joined a country club.The number of times you expect to play golf in a month is represented by a random variable with a mean of 10 and a standard deviation of 2.2.Assume you pay monthly membership fees of $500 per month and pay an additional $50 per round of golf.
What is your average monthly bill from the country club?

A)$700
B)$800
C)$900
D)$1000

Question 25

The mean of a normally distributed group of weekly incomes for a group of executives is $2,400 and the standard deviation is $600.What is the z-score for an income of $1,500/week?

A)-1.5
B)-1.0
C)2.5
D)1.9

Question 26

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Let the random variable X follow a normal distribution with a mean of 17.1 and a standard deviation of 3.2.
What is P(X > 16)?

A)0.3401
B)0.6331
C)0.3669
D)0.8326

Question 27

Let the random variable Z follow a standard normal distribution.Find the value k,such that P(Z > k)= 0.73.

A)0.27
B)0.73
C)-0.16
D)-0.61

Question 28

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Let the random variable Z follow a standard normal distribution.
What is P(0.33 < Z < 0.45)?

A)0.5443
B)0.0443
C)0.4557
D)0.1515

Question 29

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Let the random variable X follow a normal distribution with a mean of 61.7 and a standard deviation of 5.2.
What is the value of k such that P(59 < X < k)= 0.54?

A)65.8
B)64.6
C)63.7
D)66.9

Question 30

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Let the random variable Z follow a standard normal distribution.
What is P(Z > -0.21)?

A)0.4207
B)0.4168
C)0.5793
D)0.5832

Question 31

Which of the following is false regarding the normal distribution?

A)The mean,median,and mode are equal.
B)The frequency of values peaks at the mean,regardless of the value of the mean or variance.
C)100% of the values fall between ±3 standard deviations.
D)The shape of the distribution is symmetrical around the mean.

Question 32

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Let the random variable X follow a normal distribution with a mean of 61.7 and a standard deviation of 5.2.
What proportion of the total area under the normal curve is within ± two standard deviations of the mean?

A)About 50%
B)About 68%
C)About 95%
D)About 99.7%

Question 33

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
You have recently joined a country club.The number of times you expect to play golf in a month is represented by a random variable with a mean of 10 and a standard deviation of 2.2.Assume you pay monthly membership fees of $500 per month and pay an additional $50 per round of golf.
What is the standard deviation for your average monthly bill from the country club?

A)$220
B)$110
C)$324
D)$180

Question 34

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Let the random variable Z follow a standard normal distribution.
What is P(Z > 1.2)?

A)0.1112
B)0.8849
C)0.1151
D)0.6112

Question 35

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Let the random variable X follow a normal distribution with a mean of 17.1 and a standard deviation of 3.2.
What is P(15 < X < 20)?

A)0.5581
B)0.1814
C)0.5640
D)0.2546

Question 36

Let the random variable Z follow a standard normal distribution.Find the value k,such that P(-0.62 < Z < k)= 0.43.

A)0.20
B)0.52
C)0.12
D)0.56

Question 37

The normal probabilities are calculated using the table of standard normal distribution where the mean and standard deviations are,respectively:

A)1 and 1.
B)10 and 0.
C)0 and 1.
D)0 and 10.

Question 38

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Let the random variable X follow a normal distribution with a mean of 61.7 and a standard deviation of 5.2.
What is the value of k such that P(X > k)= 0.63?

A)59.984
B)66.446
C)62.830
D)67.576

Question 39

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Let the random variable Z follow a standard normal distribution.
The distribution of annual incomes of a sample of college graduates is normally distributed with a mean of $52,000 and a standard deviation of 1,000.About 68 percent of the incomes lie between what two income levels?

A)52,000 and 62,000
B)50,000 and 60,000
C)51,000 and 53,000
D)53,000 and 57,000

Question 40

Investment A has an expected return of 7.8% with a standard deviation of 2%.Investment B has an expected return of 7.2% with a standard deviation of 3.1%.Which stock is more likely to have a return greater than 10%?

A)Stock A
B)Stock B
C)The probability is the same for both A and B.
D)Unable to determine.

Question 41

Let X₁,X₂,...... ,X_k be a set of k continuous random variables.The function F(x₁,x₂,..... ,x_k)which defines the probability that simultaneously X₁ < x₁,X₂ < x₂ and so on is called a:

A)marginal distribution function.
B)marginal cumulative distribution function.
C)joint cumulative distribution function.
D)normal distribution function.

Question 42

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Investment A has an expected return of 8% with a standard deviation of 2.5%.Investment B has an expected return of 6% with a standard deviation of 1.2%.Assume you invest equally in both investments and that the rates of return are independent.
What is the standard deviation of the return on your portfolio? Assume that the returns on the two investments are independent.

A)2.77
B)2.50
C)7.69
D)6.25

Question 43

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
You are the webmaster for your firm's web-site.From your records,you know that the probability that a visitor will buy something from your firm is 0.23.In one day,the number of visitors is 952.
What is the probability that at least 210 of them will buy something from your firm? Use the normal approximation to the binomial.

A)0.7549
B)0.2549
C)0.2451
D)0.7451

Question 44

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The number of orders that come into a mail-order sales office each month is normally distributed with a mean of 298 and a standard deviation of 15.4.
The probability is 0.3 that the sales office receives less than how many orders?

A)310.9
B)285.1
C)290.0
D)306.0

Question 45

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The number of orders that come into a mail-order sales office each month is normally distributed with a mean of 298 and a standard deviation of 15.4.
What is the probability that in a particular month the office receives more than 310 orders?

A)0.7823
B)0.2826
C)0.7174
D)0.2177

Question 46

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The amount of time you have to wait at a particular stoplight is uniformly distributed between zero and two minutes.
The median score for the final exam in a chemistry class was 75 and 18% of the students received a grade greater than 80.If the test scores were normally distributed,what is the probability that a randomly selected exam had a score between 75 and 80?

A)68%
B)32%
C)80%
D)50%

Question 47

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The length of time it takes to be seated at a local restaurant on Friday night is normally distributed with a mean of 15 minutes and a standard deviation of 4.75 minutes.
A fair coin is flipped 100 times.The probability of obtaining between 40 and 60 heads is approximately:

A)0.6826
B)0.7518
C)0.9544
D)0.9973

Question 48

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
You are the webmaster for your firm's web-site.From your records,you know that the probability that a visitor will buy something from your firm is 0.23.In one day,the number of visitors is 952.
What is the probability that less than 200 of them will buy something from your firm? Use the normal approximation to the binomial.

A)0.4279
B)0.5721
C)0.9279
D)0.0721

Question 49

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The amount of time you have to wait at a particular stoplight is uniformly distributed between zero and two minutes.
What is the probability that you have to wait more than 30 seconds for the stoplight?

A)0.25
B)0.50
C)0.75
D)1.01

Question 50

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The number of orders that come into a mail-order sales office each month is normally distributed with a mean of 298 and a standard deviation of 15.4.
What is the area under the normal curve between Z = 1.0 and Z = 2.0?

A)0.0228
B)0.1359
C)0.3413
D)0.4772

Question 51

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The length of time it takes to be seated at a local restaurant on Friday night is normally distributed with a mean of 15 minutes and a standard deviation of 4.75 minutes.
What is the probability that you have to wait between 13 and 16 minutes to be seated?

A)0.083
B)0.246
C)0.163
D)0.663

Question 52

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The length of time it takes to be seated at a local restaurant on Friday night is normally distributed with a mean of 15 minutes and a standard deviation of 4.75 minutes.
What is the probability that you have to wait more than 20 minutes to be seated?

A)0.1761
B)0.3531
C)0.6761
D)0.1469

Question 53

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The amount of time you have to wait at a particular stoplight is uniformly distributed between zero and two minutes.
Eighty percent of the time,the stoplight will change before you have to wait X seconds,what is the value of X?

A)90 seconds
B)24 seconds
C)30 seconds
D)96 seconds

Question 54

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The amount of time you have to wait at a particular stoplight is uniformly distributed between zero and two minutes.
Sixty percent of the time,the stoplight will change before you have to wait X seconds,what is the value of X?

A)72 seconds
B)60 seconds
C)48 seconds
D)36 seconds

Question 55

Let the random variable Z follow a standard normal distribution.Find the value k,such that P(-k < Z < k)= 0.78.

A)1.78
B)1.37
C)1.23
D)0.78

Question 56

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Investment A has an expected return of 8% with a standard deviation of 2.5%.Investment B has an expected return of 6% with a standard deviation of 1.2%.Assume you invest equally in both investments and that the rates of return are independent.
What is the expected return of your portfolio?

A)8%
B)7%
C)6%
D)4%

Question 57

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Investment A has an expected return of 8% with a standard deviation of 2.5%.Investment B has an expected return of 6% with a standard deviation of 1.2%.Assume you invest equally in both investments and that the rates of return are independent.
A hospital finds that 20% of its accounts are at least 60 days in arrears.A random sample of 500 accounts was taken.What is the probability that fewer than 120 accounts in the sample were at least 60 days in arrears?

A)0.9875
B)0.4875
C)0.5125
D)0.0125

Question 58

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The amount of time you have to wait at a particular stoplight is uniformly distributed between zero and two minutes.
What is the probability that you have to wait between 15 and 45 seconds for the stoplight?

A)0.15
B)0.25
C)0.35
D)0.45

Question 59

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The number of orders that come into a mail-order sales office each month is normally distributed with a mean of 298 and a standard deviation of 15.4.
What is the area under the normal curve between Z = -2 and Z = 0?

A)0.5000
B)0.6826
C)0.1359
D)0.4772

Question 60

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The number of orders that come into a mail-order sales office each month is normally distributed with a mean of 298 and a standard deviation of 15.4.
What proportion of the total area under the normal curve is above the mean?

A)50%
B)68%
C)95%
D)99.7%

Question 61

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The time it takes to assemble an electronic component is normally distributed with a mean of 17.2 minutes and a standard deviation of 3.1 minutes.
The probability is 95% that it will take at least how long to assemble a component?

A)12.7
B)11.7
C)12.1
D)11.1

Question 62

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Let X be a continuous random variable with mean of 1200 and standard deviation of 250.Define the random variable Y as follows: Y = 80 + 0.05X
What is the standard deviation of Y?

A)92.5
B)55.9
C)12.5
D)11.89

Question 63

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The number of nails in a five-pound box of nails is normally distributed with a mean of 563.3 and a standard deviation of 33.2.
What is the probability that there are less than 500 nails in a randomly-selected five-pound box of nails?

A)0.5287
B)0.4730
C)0.0281
D)0.9713

Question 64

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The time it takes to assemble an electronic component is normally distributed with a mean of 17.2 minutes and a standard deviation of 3.1 minutes.
What is the probability that it will take at least 16 minutes to assemble a component?

A)0.8483
B)0.3483
C)0.1517
D)0.6517

Question 65

Checkout times in a Walmart store follow an exponential distribution with a mean time of 8 minutes.What is the probability that the checkout time for the next customer will be 6 minutes or less?

A)0.528
B)0.472
C)0.972
D)0.328

Question 66

The probability is 0.99 that a randomly-selected five-pound box of nails contains at least how many nails approximately?

A)641
B)486
C)503
D)624

Question 67

A two-dimensional plot of the observed data values on the vertical-axis with their corresponding quartile values from a standardized normal distribution on the horizontal-axis is referred to as a:

A)normal probability plot.
B)quartile plot.
C)normal probability distribution.
D)normal-quartile plot.

Question 68

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Sales at a local wholesaler consist of both retail as well as online sales.During the course of a month,retail sales have a mean of $96,780 with a standard deviation of $12,520.Over the same time period,online sales average $229,620 with a standard deviation of $23,100.Assume that the retail sales are independent of online sales.
A car owner determines that annual repair costs (R)can be estimated based on the number of miles driven in one year (M)through the expression R = 800 + 0.05M.If the average number of miles driven is 12000 with a standard deviation of 2500 miles,what is the standard deviation of the expected annual repair costs?

A)1400
B)925
C)800
D)125

Question 69

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Sales at a local wholesaler consist of both retail as well as online sales.During the course of a month,retail sales have a mean of $96,780 with a standard deviation of $12,520.Over the same time period,online sales average $229,620 with a standard deviation of $23,100.Assume that the retail sales are independent of online sales.
What is the mean of the wholesaler's monthly sales?

A)$326,400
B)$135,620
C)$132,840
D)$163,200

Question 70

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The time it takes to assemble an electronic component is normally distributed with a mean of 17.2 minutes and a standard deviation of 3.1 minutes.
The median score for the final exam in a statistics class was 85 and 20 percent of the students received a grade greater than 90.What is the probability that a randomly selected exam had a score between 85 and 90?

A)80 percent
B)30 percent
C)50 percent
D)There is not sufficient information to answer this question.

Question 71

The speed of cars passing through a check point follows a normal distribution with a mean of 45 miles per hour and a standard deviation of 6 miles per hour.What is the probability that the next car passing will be exceeding 51 miles per hour?

A)0.9854
B)0.8413
C)0.7967
D)0.1587

Question 72

Let the random variable Z follow a standard normal distribution.The total probability to the right of Z = 2.18 and to the left of Z = -1.75 is:

A)0.4854
B)0.4599
C)0.0146
D)0.0547

Question 73

Let the random variable Z follow a standard normal distribution,and let z₁ be a possible value of Z that is unknown but identifiable by position and area.Find z₁ if the area to the right of z₁ is 0.8413.

A)1.00
B)-1.00
C)0.00
D)0.41

Question 74

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
The number of nails in a five-pound box of nails is normally distributed with a mean of 563.3 and a standard deviation of 33.2.
What is the probability that there are between 525 and 575 nails in a randomly-selected five-pound box of nails?

A)0.5117
B)0.4883
C)0.5526
D)0.4474

Question 75

Given that X is a normally distributed random variable with a mean of 52 and a standard deviation of 2,the probability that X is between 48 and 56 is:

A)0.0896
B)0.4104
C)0.5896
D)0.9544

Question 76

Which type of distribution would best model the waiting times of the departing flights at JFK international airport?

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

Question 77

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

A)It is symmetrical distribution.
B)The mean is always zero.
C)The mean,median,and mode are all equal.
D)It is a bell-shaped distribution.

Question 78

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Sales at a local wholesaler consist of both retail as well as online sales.During the course of a month,retail sales have a mean of $96,780 with a standard deviation of $12,520.Over the same time period,online sales average $229,620 with a standard deviation of $23,100.Assume that the retail sales are independent of online sales.
What is the standard deviation of the wholesaler monthly sales?

A)$35,620.0
B)$26,274.7
C)$71,240.0
D)$68,960.3

Question 79

During a professor's office hours,students arrive,on average,every ten minutes.Assume that the distribution of the time between arrivals follows an exponential distribution.Suppose that a student has just left. What is the probability that the professor has more than 20 minutes before the next student shows up?

A)0.8187
B)0.8647
C)0.1353
D)0.1813

Question 80

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION:
Let X be a continuous random variable with mean of 1200 and standard deviation of 250.Define the random variable Y as follows: Y = 80 + 0.05X
What is the mean of Y?

A)680
B)330
C)120
D)140