Business Math And Statistics

Front 1

The Gofast Tire and Rubber Co. is thinking about producing a new tire. Mangement has been presented a detailing of costs for the purchasing and production departments as follows:
Direct Labor ... $2/tire
Rubber ... $7/tire
Steel Belts ... $4/tire
Modification to Factory ... $2,000,000
New Machinery ... $5,000,000
What are the total costs for the first year, assuming management buys all necessary equipment, makes modifications and plans to product one million tires

Back 1

[(2+7+4)*1,000,000] +2,000,000+5,000,000=
2,000,000

Front 2

Y=X^2 -9 is a parabola which

Back 2

Has a minimum at X=0
At x^2=0, y=9
Since the curve is sloping upward at y=-9, there is a minimum at x=0

Front 3

Solve for x: (2x +3)/5 + (x+1)/4=2

Back 3

(2x+3)/5 + (x+1)/4=2
5(2x+3)/5 + 5(x+1)/4=10
2x+3+5(x+1)/4=10
8x + 12 +20(x+1)/4 = 40
8x + 12 + 5(x+1) = 40
8x + 12 + 5x + 5 = 40
13x=23
x=23/13

Front 4

Which of the following is the correct form for separating and ordering equations NOT being used:
a) (5*20) + [(8/4)*17]/5
b) 7/([19/(14+20)] + (14*(18+20y)))
c) [(5y+19)*7]/(9y+59(/7]
d) none of the above

Back 4

B
The order given for separating, ordering and organizing expressions is: parentheses, brackets, braces, parentheses (if necessary), etc. B does not follow this pattern

Front 5

Corner Office Seating builds an executive office chair. The variable costs to produce the chair are $150/chair, the chair is sold by Corner Office to its wholesalers for $350, then the wholesalers sell to office furniture stores for $450, which sell to the final customer for $800. The fixed costs for production of the chair are $3,000,000 per year. How many chairs will Corner Office have to sell each year in order to break even on this product?

Back 5

First find the contribution margin, sales minus variable costs: (350)-(150) = $200.
Second, calculate the break-even analysis by taking the fixed costs and divide by the contribution margin: 3,000,000/$200 = 15,000 units

Front 6

Break Even Analysis

Back 6

Total fixed costs divided by the contribution margin per unit.

Front 7

Contribution Margin Definition and Equation

Back 7

the amount a company receives from the sale of its product minus its variable costs
aka the costs directly associated with producing the product. Can be used to pay fixed costs. Once fixed costs are covered the contribution margin is a profit.

Front 8

Lawnmaster, Inc. recently started building a new riding lawnmower. In the first year of production (1996) Lawnmaster built 250,000 and sold 175,000. The variable costs that year were $575/unit, and the retail price was $1,400 (sold to wholesalers for $900/unit). The fixed costs necessary to start production were $50,000,000. What was the contribution margin per unit?

Back 8

Contribution margin is sales-variable costs: 900-575=325

Front 9

What is the vertex of the equation: y=3x^2 - 24x + 21

Back 9

(4,-27)
First, locate the intercepts. (1,0) and (7,0)
The axis of symmetry of the parabola runs right through the middle of the two points where x=4. Solve for y when x is 4 gives a y of -27. That means the vertex is (4,-27)

Front 10

The expression 27x^5y^3/3x^2y can be simplified to

Back 10

9x^3y^2

Front 11

Solve for x:
5x^2-7x-1=4x^2-11x-4

Back 11

5x^2-7x-1=4x^2-11x-4
5x^2-7x-4x^2+11x=-3
x^2+4x=-3
x^2+4x+3
(x + 3)(x+ 1)
x=-3, x= -1

Front 12

A man buys 3 burgers and 2 jumbo deluxe fries for $7.40. A woman buys one burger and 4 jumbo deluxe fries for $7.80. How much is the burger and how much are the fries?

Back 12

3x+2y=7.40
x+4y=7.80
First, make one of the exponents common
3x+2y=7.40
3(x+4y) = 3(7.80)
3x+2y=7.40
3x + 12y = 23.40
Then subtract
0-10y=-16
Solve for y=1.6
Then replace y with 1.6
3x + 2(1.6) = 7.40
3x + 3.2 = 7.40
3x = 4.20
x=1.40

Front 13

When gathering time series data for a trend analysis, it is important to collect the data at the same time each period because

Back 13

it's easier to remember, it reduces variation and it increases accuracy

Front 14

True or false, in the weighted average technique, all of the examples given in the text placed heavier weights on more recent data.

Back 14

True. Heavier weights are placed on the more recent data because the underlying assumption is that these data are the most relevant.

Front 15

Samantha kept track of the sales of a specific brand and color of paint sold in her store for one month. What would be a reasonable estimate for the daily average of number of gallons of this paint she will sell next month?
#Days ... #Gal Sold
12 ... 13
6 ... 16
9 ... 18
2 ... 22
1 ... 25

Back 15

(25(1) + 22(2) + 18(9) + 16(6) + 13(12))/30
(25+44+162+96+156)/30
483/30
16.10

Front 16

Given the following time series data, you would forecast with what method?
110, 120, 130, 140, 150

Back 16

Trend line data

Front 17

Trend time series analysis is good if ...

Back 17

the pattern shows a steady increase or decrease over time

Front 18

The average analysis of data is good if ...

Back 18

the data samples are recent and don’t vary too much because this process considers each piece of data equally to the rest.

Front 19

Moving average is good if ...

Back 19

data extends WAY back and is subject to periods of radical change. This technique only uses a sample of the data. Computes difference between what you forecasted last time and what actually happened. Very similar to simple average so it basically has the same advantages and disadvantages.

Front 20

Weighted average is good if ...

Back 20

you want to weigh some data as being more relevant than others, but it's subject to personal bias.

Front 21

Calculation of weighted average

Back 21

Y=ΣwY/Σw
where w is the weight given to each individual data sample Y is the weighted average, Σ represents the process of addition or summation (note that the w and Y are multiplied
together before all of the values are summed together), and Y is the value of each data sample to be averaged.

Front 22

True or false, if you wanted a more accurate way to fit the trend line to the data, a method called least squares could be used. This method finds the largest distance between the data points and the trend lines.

Back 22

False.

Front 23

Define the least squares method

Back 23

Minimizes the distance of data points to the trend line. The points that are not on the line have a certain measurable deviation from the line.

Front 24

A weighted moving average having the early periods weighted more heavily ...

Back 24

is less responsive to recent demand changes.

Front 25

Weighted moving average

Back 25

tends to weight heavily the most recent periods because this weighting would be more responsive to recent demand changes.

Front 26

Using a 3-month moving average forecast with the following data, what is the forecast for Dec.?
Month ... Hot Chocolate Sales (in 1000s)
May ... 13
June ... 16
July ... 17
August ... 18
Sept. ... 20
Oct. ... 21
Nov. ... 23

Back 26

(20 + 21 +23)/3
=64/3
21.33

Front 27

The idea behind weighting the most recent data most heavily is

Back 27

The most recent data contains the best information

Front 28

When analyzing data where a steady increase or decrease over time can be observed, which method of forecasting would best fit and would probably predict a similar increase or decrease?

Back 28

Trend analysis method because it is most appropriate when increases or decreases are evident.

Front 29

Which of the following statements is false?
a) Simple averaging considers all data samples equally.
b) using simple averaging when the data samples have a lot of variability will provide accurate forecasts
c) simple averaging is easy to understand and apply
d) none of the above

Back 29

b) using simple averaging when the data samples have a lot of variability will provide accurate forecasts

Front 30

The number of automobile accidents in a certain region are related to the regional number of registered automobiles in tens of thousands (b1), alcoholic beverage sales in $10,000 (b2), and the decrease in the price of gasoline in cents (b3). Imagine the regression formula has been calculated as: Y=a+b1X1+b2X2+bX3
where Y=the number of automobile accidents, a=7.5, b1=3.5, b2=4.5, and b3=2.5.
Calculate the expected number or automobile accidents for a football weekend if the region has 25,000 registered vehicles, $75,000 worth of beer is sold, and a gas war causes a .10 drop in a gallon of gas.

Back 30

Y=a+b,x,+b2X2+b3X3
=7.5 + 3.5(2.5) + 4.5 (7.5) + 2.5(10)
=75.00

Front 31

True or false, if the correlation coefficient for a multiple regression equation is significant, all independent variables are required for regression.

Back 31

False. The number of independent variables is not necessarily related to the correlation coefficient. Data could show a large number for r, but a fairly small number of independent variables.

Front 32

Correlation coefficient

Back 32

measures the strength of a linear relationship

Front 33

Which of the following is not an assumption for simple linear regression?
a) the mean of each error component is zero
b) each error component follows an approximate normal distribution
c) the error components lie on a straight line
d) the variance for the error components is the same for each value of X

Back 33

c) The error components lie on a straight line
The error components are random and do not lie on a straight line

Front 34

Edna's T-ratio is less than 2 for the constant term in her regression equation so she should be

Back 34

not very concerned. T-statistics less than 2 are an area of concern for the coefficients of the independent variable because they may indicate a 0 coefficient. A 0 coefficient means there is no relationship between the independent and dependent variables. The constant term has no particular significance to the analyst and can have a low T-ratio

Front 35

T-statistics less than 2 are

Back 35

an area of concern for the coefficients of the independent variable because they may indicate a 0 coefficient.

Front 36

A 0 coefficient means

Back 36

there is no relationship between the independent and dependent variables.

Front 37

The constant term can have a high or low T-ratio

Back 37

Low because it has no particular significance to the analyst

Front 38

A real estate agent says he can approximate the value of a house through the following equation:
SP=125,000 + 3000(#bathrooms) + 500(#bedrooms) +4000(winecellar) - 6000(pool).
There are ____ zero-one variable in this regression model

Back 38

There are 2 zero-one variables in the regression model, wine cellar and pool. You either have it or you don't

Front 39

A zero-one variable is like ...

Back 39

a yes or no question

Front 40

True or false, a low T-ratio for the coefficient of an independent variable is a concern because it indicates the true coefficient may be 0 or close to zero?

Back 40

True.

Front 41

The T-ratio measures ...

Back 41

The number of standard deviations from 0 of the coefficient of the independent variable.

Front 42

Jamie's regression equation shows a correlation between X3 (the T-ratio is 5) and X4 (the T-ratio is 12) of .4. He should ...

Back 42

Keep both because the T-ratios are large, indicating believable coefficients for X3 and X4.

Front 43

Multicollinearity

Back 43

When two factors have high T-ratios/correlation

Front 44

If you have a coefficient of determination .49, in simple regression what is the coefficient of correlation?

Back 44

+ or - .7
It is impossible to determine whether the independent variable(s) is positively or negatively correlated with the dependent variable.

Front 45

A regression equation has the formula:
Y'=15X4 + 7X3 + 12X2 + 1.07X1 + 5
Which of these is the dummy variable?

Back 45

Ignore the regression line. Soil grade (fertile or infertile) is only one of two values so it's the dummy variable.

Front 46

A real estate agent says he can approximate the value of a house through the following equation:
SP=125,000 + 3000(#bathrooms) + 500(#bedrooms) +4000(winecellar) - 6000(pool).
If the owners of the house want to increase its value by the most possible they should:

Back 46

Fill the pool. It would eliminate the biggest expense if all the options are discrete.

Front 47

Two independent pollsters surveyed the same number of people from two different populations of approx. equal size. Pollster A concluded he was the 95% confident the mean weight of his populations was 150+16.3 pounds. Pollster B concluded she was 95% confident the mean of her population is 150 + 11.6 pounds. Which of the following statements is true.
a) A randomly selected person from Pollster A's population is more likely to weight between 145 and 155 than Pollster B's pop.
b) People in the pop. Pollster A surveyed are less alike in weight than those in the population surveyed by Pollster B.
c) The standard deviation of both populations is the same
d) The standard error of both populations is the same

Back 47

b) People in the pop. Pollster A surveyed are less alike in weight than those in the population surveyed by Pollster B.
11.6 is less than 16.3 So we can conclude the dispersion is greater than A.

Front 48

An advertising firm has five prospective clients whose business it is trying to attract. The managing partner is considering offering these clients reduced rate on media time she has purchased. She reasons each client is just as likely to sign on with the firm given these circumstances. The best tool to use to determine the probability that at least one client will sign is ...

Back 48

Binomial distribution because the chance of winning a client (designated success) is the same for each of the potential clients, the act of winning a client can best be represented by a Bernoilli Trial and the probability to winning one or more can be obtained using the binomial distribution probability table.

Front 49

Joint probability

Back 49

the probability of two events occurring together, forexample, an ace that is a spade , written P(Ace,space) or P(spade,ace).

Front 50

Normal distribution

Back 50

the probability distribution for a number of random variables is a normal bell-shaped curve. Best used when each data point represents a sum or average of some other bits of data.

Front 51

Cumulative distribution function

Back 51

considers the possibility that the outcome will be less than or equal to a certain value.

Front 52

Binomial distribution

Back 52

the distribution of the number of successes in a string of Bernoulli Trails

Front 53

Bernoulli Trial

Back 53

An event that has two possible outcomes: one a success and one a failure. Flipping a coin is an example.

Front 54

Probability Mass Function

Back 54

limited number of outcomes and the decision maker assigns probabilities to each of those outcomes. These outcomes still need to be mutually exclusive and collectively exhaustive. Each outcome should have a number and the sum of probabilities should equal 100%, or the decision maker is 100% positive one of these outcomes will occur.

Front 55

True or false, the type of probability described in the statement "the probability of randomly-selected person having brown hair is 80% if it is a woman" is a conditional probability.

Back 55

True

Front 56

Conditional probability

Back 56

the probability of one event occurring conditional upon another that is already known or has already occurred.

Front 57

A real estate developed is trying to determine how many homes she will sell in her brand new development next month. Her sales manager gives her the following probability for several levels of home sales, but accidently leaves one off. What is the probability that three homes or more will be sold next month, expressed as a decimal:
Homes sold ... Probability
0 ... .25
1 ... .31
2 ... .18
3 ... .17
4 ...

Back 57

Sum of probabilities must add to 1.
.25+.31+.18+.17+x=1
x=.09 (The probability of selling 4 houses)
THEN add to the prior probability: .17+.09=.26 or 26%

Front 58

Cooper Realty is a small real estate co. specializing in residential listings. They recently became interested in determining the likelihood one of their listings being sold within a certain number of days. An analysis of company sales of 800 homes in previous years produced the following data. What is the probability that a home listed for more than 90 days before being sold out? Total number of days until sold for varying prices for houses listed more than 90 days is 200 days
a).75
b).66
c).50
d).25

Back 58

200 days/800 homes = .25

Front 59

A survey among entrepreneurs indicates the average number of hours worked per week is normally distributed with a mean of 60 hours and a standard deviation of 15 hours. What is the probability the next entrepreneur surveyed will work less than 30 hours per week?

Back 59

Check the normal probability distribution table in Appendix C. The z-score is -2 determined by (30 hours per week-60 hours per week)/15 hours and the corresponding probability is .02275 or 2.275%

Front 60

Illustration 7 in the back of the text shows a normally distributed curve for shotput throws along with its mean and standard deviation. What is the probability that the next shotput throw will travel 23.75 yards or more?

Back 60

The mean of shotput distances is 30 yards with a standard deviation of 5. You know 23.75 yards is 1.25 standard deviations (z-score=(23.75/5)=-1.25) bellow the mean. Look up 1.25 in the normal distribution table and see 0.10565 probability the next shotput thrown will go less than 23.75 yards, since 23.75 is below the mean subtract .10565 from 1 for .89435 for a .894 probability it will go 23.75 yards or more.

Front 61

The ages of personnel in the accounting department of a large co. are normally distributed with a standard deviation of 7 years. There is a .02275 probability that the age of any randomly chosen person in the department is less than 22 and a .15866 probability the age of any person is greater than 43. What is the mean of distribution?

Back 61

36. Find corresponding z-score of each probability and multiple z-score by the standard deviation to find the distance from the point to the mean.
The probability of .02275 corresponds to a z-score of 2. Multiple 2 by the standard deviation of 7 to get 14, which is how far the point of 22 is below the mean. Thus, the mean of distribution is 22+14=36

Front 62

What is the mean of the following probability distribution?
99 ... .16
100 ... .21
101 ... .34
102 ... .23
103 ... .06

Back 62

100.82. Multiple each outcome by the probability of it occurring and then sum them all together

Front 63

How do you find the mean of a probability distribution?

Back 63

Multiple each outcome by the probability of it occurring and then sum them all together

Front 64

True or false, if you have a litter of 6 puppies (2 female and 4 male) and randomly select a puppy the events that the puppy is female and the puppy is male are mutually exclusive?

Back 64

True. The outcomes cannot occur at the same time.

Front 65

Outcomes are mutually exclusive if ...

Back 65

they cannot occur at the same time

Front 66

The value of an event node is ...

Back 66

the expected value of the branches emanating from it. Each branch has a value plus a probability which gives it an expected values.

Front 67

True or false, the decision maker determines which branch to follow from an event node

Back 67

False.

Front 68

True or false, the decision maker determines which branch to follow from an decision node

Back 68

True

Front 69

Which of the following would best be represented by a decision node?
a) Bob rides a cab or a bus to work, whichever he can find most quickly
b) Sal either wins or doesn't win the lottery
c) Jill goes to work for one of two firms who have offered her a position
d) none of the above

Back 69

c) Jill goes to work for one of two firms who have offered her a position

Front 70

To determine the proper sequence of decisions

Back 70

begin with the last nodes. Begin with the last nodes in a "branch" and work your way back to the trunk of the decision tree

Front 71

A decision node is represented by a(n) _____ and an event node by a(n) ____.

Back 71

Square, circle.

Front 72

Three branches emanate from an event node. Their end values are $25 with a probability of .50 occurring, $30 with a probability of .25 occurring, and $40 with a probability of .25

Back 72

(25*0.5)+(30*0.25)+(40*0.25)=30

Front 73

A market research survey is available for $10,000. Using a decision tree analysis, it is found the expected monetary value with the survey is $65,000. The expected monetary value with no survey is $62,000. What is the expected value of information from this sample.

Back 73

3,000. The difference between the survey and no survey.

Front 74

True or false, the expected monetary value of EMV is a number based on averaging.

Back 74

True.

Front 75

How do you derive EMV?

Back 75

Multiply probabilities by outcomes and add them up.

Front 76

Which of the following nodes could be combined into one?
a) If Jay decides to go out to lunch, he has to decide where to go.
b) After Jay decides to go out to lunch, he has to make sure he has a meeting, and if he doesn't, decide where he wants to go to lunch.
c) Jay finds out whether he has a meeting, then decides whether to go out to lunch
d) none of the above.

Back 76

A. It's two DECISION nodes, so it can be combined

Front 77

Tim has not been doing well in statistics class. His professor tells him to write up a case analysis for her in order to pass the class. He can still pass the class without the write-up, just like he can still fail with it, since the final exam is coming up. Which of these decisions would have a vertical line at the end of their branch?
a) do nothing (don't write the case analysis)
b) pass the final exam
c) write the case analysis
d) none of the above

Back 77

None of the above. All of the options presented represent outcomes or alternatives that have other nodes following them.

Front 78

parabola

Back 78

an equation that has two x's for every y

Front 79

axis of symmetry

Back 79

the invisible line that cuts a parabola in half

Front 80

vertex

Back 80

the point at which the axis of symmetry intersects a parabola

Front 81

a vertex is a U if

Back 81

x^2 is positive

Front 82

a vertex is an upside-down U if

Back 82

x^2 is negative

Front 83

vertex calculation

Back 83

-b/2a is the x value, then substitute that number as the x coordinate to find the y value

Front 84

To find the value of b in the least-squares trend line

Back 84

b=(EXY-((EX*EY)/n))/(EX^2-(((EX)^2)/n)

Front 85

The find the slope of the regression line

Back 85

first find b in the least-squares trend line:
b=(EXY-((EX*EY)/n))/(EX^2-(((EX)^2)/n)
Then determine where b crosses the y axis.
First, find average of Y
Then, find average of X
Then, Average of Y=a+b(average of X)

Front 86

regression line reveals

Back 86

nature of relationship between X and Y but NOT how strong the relationship is; it can explain most of the variation from the regression line

Front 87

coefficient of determination

Back 87

tells us how much variation in the data can be explained by a regression model

Front 88

basic underlying premise of the time series technique of averaging

Back 88

any given Y value will coincide the Ybar because Ybar is the average of all past Y values and a good indication of future ones.

Front 89

coefficient of determination

Back 89

percentage of variation explained by regression model.

Front 90

calculation of coefficient of determination

Back 90

r^2=explained variation/total variation

Front 91

calculation of correlation coefficient is

Back 91

r=+or- square root of r^2

Front 92

a positive correlation coefficient means

Back 92

as X increases so does why, and vice versa

Front 93

T-ratio

Back 93

measure of the significance of each of the independent variables

Front 94

T-ratio tells you

Back 94

how many standard deviations away from zero the coefficient of your independent variable is

Front 95

The standard deviation and the variance are measures of

Back 95

spread or dispersion

Front 96

variance is measured by

Back 96

the square of the standard deviation

Front 97

Standard deviation is calculated by

Back 97

the square root of the sum of the squared differences from the mean multiplied by the probability of their outcomes.
First: calculate the mean (sum of each occurrence times its probability)
Second: Take the mean, subtract the each occurrence, square it and then multiple it by its probability, then add all of that up
Fourth: take the square root of the summation

Front 98

The larger the standard deviation

Back 98

the more spread out the distribution

Front 99

z-score

Back 99

the difference between the mean and the amount in question divided by the standard deviation

Front 100

z-score helps measure

Back 100

probability that the next data point is the same size, smaller, or larger

Front 101

if your z-score point is below the mean

Back 101

that's the probability the next data sample will be less