C723 - Formulas and Samples

P(event) = (the number of occurences of an event divded by number of trials) What is that formula used to determine?

the probability

What would be the additional cost to crash Activity A by the maximum time reduction period? Normal days = 12 Normal cost = $18,000 Crash days = 8 Crash cost = $22,000 Maximum time reduction = 4

(22,000 - 18,000) ÷ (12 - 8) 4,000 ÷ 4 = 1,000 1,000 x 4 = 4,000 The answer is $4,000

Based on Activity A as described below, what would be the cost to crash by 2 days be? Normal days = 12 Normal cost = $18,000 Crash days = 8 Crash cost = $22,000 Maximum time reduction = 4

(22,000 - 18,000) ÷ (8 - 12) 4,000 ÷ 4 = 1,000 1,000 x 2 = 2,000 The answer is $2,000

Based on the graphic below, what would be the additional cost to crash Activity C by the maximum time reduction period? Normal days = 20 Normal cost = $32,000 Crash days = 12 Crash cost = $38,000 Maximum time reduction = 8

(38,000 - 32,000) ÷ (20-12) 6,000 ÷ 8 = 750 750 x 8 = 6,000 The answer is $6,000

Safe Driver Car Insurance company is trying to determine the probability of accidents based on age categories. The data from the previous year have been captured below: 500 Drivers under age 20 had 20 accidents 495 Drivers aged 20-39 yrs had 30 accidents 655 Drivers aged 40-59 yrs had 40 accidents 350 Drivers aged 60 and over had 25 accidents Based on this data, which age bracket has the highest probability of having an accident based on the number of drivers in the age group?

#accidents compared to #drivers for each group 20/500=.04 30/495=.06 40/655=.06 25/350=.07 60 and over has the highest probability of .07 or 7%

Project scheduling is the process of scheduling the individual tasks required to meet the project deliverables. These tasks are scheduled in a rational sequence to meet the time objectives of the project. In preparing the schedule, the duration for each of the tasks and its subtasks is estimated, thus providing a total estimated duration for each task. The sum of the duration of all the tasks is the estimated duration for the whole project. One common technique for estimating the duration of tasks is the beta distribution method. This method uses three duration estimates for the task, pessimistic, optimistic, and most likely, in order to consider variation in the final duration estimate. This method is thought to give a better final estimate for a task's duration. The beta distribution method is equal to the sum of the optimistic time estimate for the task (o), four times the most likely time (m) estimate, and the pessimistic time estimate (p); this result is then divided by six. The formula is: Te = (o + 4m + p) / 6 Calculate duration estimates for the following situation: .The store manager was in the process of remodeling the store interior and needed to know how long the store would be closed during the project. The construction manager believed that it could be done within 8 days if everything went according to plan. There is the possibility it could take up to 16 days if they ran into structural difficulties. The store manager asked if there was any way to decrease the number of days. The construction manager thought that if he focused on all resources, the project could be done in as soon as 6 days. Using the beta distribution method, what is the estimated time to complete this task?

(6 + 4(8) + 16)/6 = 9 Breakdown: 4x8 = 32 6 + 4 + 32 + 16 = 58 58 ÷ 6 = 9 The answer is 9

Solve for x -14 + 6x + 7 - 2x = 1 + 5x

-14 + 7 = -7 and 6x - 2x = 4x So far: -7 + 4x = 1 + 5x Substract 1 from each side -8 + 4x = 5x Substract 4x from each side -8 = x

Joe's Coffee took a pole of his employees to find out how many had college degrees. Joe discovered that 288 men and 36 women working for him have a college degree. And 672 men and 204 women do not have degrees. What is the probablity that a randomly selected is a women with a degree?

1200 employess divided by 36 women with degress = 0.03 or 3%

Solve for x 2(2x-4)=16

2 times 2x= 4x 2 times -4 = -8 So far: 4x -8 = 16 Add 8 to both sides 4x = 24 Divide both sides by 4 x = 6

Joe's Coffee took a pole of his employees to find out how many had college degrees. Joe discovered that 288 men and 36 women working for him have a college degree. And 672 men and 204 women do not have degrees. Of Joe's employees; how many man could have a BA degree? Calucate the anwer in a decimal form.

288 + 36 = 324 employess with degrees 672 + 204 = 876 employess without degrees. 324 + 876 = 1,200 Total employees 288/1200 = 0.24

Solve for x 3x + 2x = 12-x

3x + 2x = 5x So fa: 5x = 12-x Add x to both sides 6x = 12 Divide both sides by 6 x=2

Solve for x 14 + 5(2x-3) = 39

5 times 2x= 10x 5 times -3 = -15 So far: 14 + 10x -15 = 39 Add 15 to both sides: 14 + 10x = 54 Substract 14 from both sides 10x = 40 Divide both sides by 10 x = 4

Solve for x 5(3-x) = 10

5 times 3 = 15 5 times -x = -15 So far: 15-5x = 10 Add 5x to each side 15 = 10 + 5x Substract 10 from each side 5 = 5x Divide both sides by 5 x = 1

Solve for x 6(x-3) = 24

6 times x= 6x 6 times -3 = -18 So far: 6x -18 = 24 Add 18 to both sides 6x = 42 Divide both sides by 6 x = 7

Tom scored 80, 90, 100, and 78 on his four tests. What is the mean (average) of his scores?

87

To calculate, determine the expected value for each alternative. First, you would multiply the value of the first condition times the probability of that condition occurring. Next, repeat the calculation for each condition. Finally, add all of the results of the newly calculated values together to establish the expected value of the alternative.

= (B1 x 60%) + (C1 x 40%)

Which of the following spreadsheet equations correctly uses the "average" function for a range of cells containing values in A1 through A25? =AVERAGE(A1:A25) AVERAGE(A1:A25) =AVERAGE A1:A25

=AVERAGE(A1:A25)

Which of the following equations will return the number of values in a range of cells? =VALUES(A1:A25) =COUNT(A1:A25) =NUMBER(A1:A25)

=COUNT(A1:A25)

Which of the following equations will return the highest value in a range of cells? =HIGHVALUE(A1:A25) =MAX(A1:A25) =MAXVALUE(A1:A25)

=MAX(A1:A25)

Which of the following spreadsheet equations correctly uses the "power" function for a base of 25, raised to the power of 3? =POWER25^3 =POWER(25,3) =POWER 3,25

=POWER(25,3)

Which of the following spreadsheet equations correctly uses both the "square root" function and the "average" function to add the two calculated values? =SQRT + AVERAGE( A1:A25) =AVERAGE(A1+A25) + SQRT(A1:A25) =SQRT(25) + AVERAGE(A1:A25)

=SQRT(25) + AVERAGE(A1:A25)

test=A+(4*M)+P÷6 What does each letter stand for?

A is the optimistic time MM is the most likely time P is the pessimistic time

Find the mode of the following set of numbers: 3, 2, 2, 1, 5, 4, 3, 2.

Because 2 occurs the most, it is the mode.

___________ = (Crash Cost - Normal Cost) ÷ (Normal Duration - Crash Duration)

Cost Slope

To find the early finish, add the early start to the duration of each task.

EF = ES + Duration of each task

To determine the early finish, add the task duration to the early start.

EF = Task duration + ES

Find the median of the following list of numbers: 3, 2, 8, 4, 1, 2, 8.

First put the numbers in increasing order. 1, 2, 2, 3, 4, 8, 8. Because there are an odd number of entries in this list, the middle number, 3, is the median.

________ = Cost of Items + Total Holding Cost + Total Ordering Cost

Inventory Cost

To determine the latest start, subtract the activity duration from the latest finish.

LS = Duration - LF

Joe's Store had 15 customers today. If 7 customers purchased milk, 5 purchased bread, and 2 purchased both what would be the formula to calculate the probability that a customer would purchse milk or bread? Then also solve the problem.

P(milk) + P(bread) - P(both milk and bread) 7 customers got milk 5 customers got bread 2 customers got both 15 customers 7/15 + 5/15 - 2/15 = 10/15 or 2/3 (2 thirds)

???? = Revenue - Expenses

Profit

This is an example of the formula used to find what? (Price per pencil*number of pencils sold) - (cost to make pencil * number of pencils sold).

Profit

Slack time (SL) is calculated using the following formula:

SL=LS−ES

Solve = ((5^2) + 20) + 5(7-3)

Solve parenthese first: 1st Par: 5^2=25 So far: (25+20) + 5(7-3) 2nd Par: 25 + 20 = 45 So far: 45+5(7-3) 3rd Par: 7-3=4 So far: 45 + 5(4) 4th Par 5 x 4 = 20 45 + 20 = 65

Using the following revenue data table, calculate the weighted moving average for all four months. Round to nearest whole number: For Month #1 the Weight was 0.1 and the Revenue was 200 For Month #2 the Weight was 0.25 and the Rev was 400 Month #3 weight was 0.3 and Rev was 175 Month #4 was 0.35 and 300 What is the weighted average for all 4 months (no decimal points) ?

Solve: 0.1x200=20 0.25x400=100 0.3x175=52.5 0.35x300=105 20+100+52.5+105=277.5 The answer is 278

How is the latest start time calculated?

Subtract the task duration from the latest finish.

Safe Driver Car Insurance company is trying to determine the probability of accidents based on age categories. The data from the previous year have been captured below: 500 Drivers under age 20 had 20 accidents 495 Drivers aged 20-39 yrs had 30 accidents 655 Drivers aged 40-59 yrs had 40 accidents 350 Drivers aged 60 and over had 25 accidents Based on this data, what is the probability of an accident occurring when members are under 40?

The Total # of accidents compared to the total # of accidents for all age groups under 40 50/115 = 0.43 or 43%

Safe Driver Car Insurance company is trying to determine the probability of accidents based on age categories. The data from the previous year have been captured below: 500 Drivers under age 20 had 20 accidents 495 Drivers aged 20-39 yrs had 30 accidents 655 Drivers aged 40-59 yrs had 40 accidents 350 Drivers aged 60 and over had 25 accidents Based on this data, what is the probability that an accident will not involve the 60 and over age group?

The Total # of accidents compared to the total # of accidents for all age groups under 60 90/115 = 0.78 or 78%

Using the following sales data table, Month #1 the Weight was 0.2 and Sales were 200 Month #2 weight was 0.25 and sales 400 #3 weight 0.25 and sales 175 Month #4 weight is unknown and sales were 300 What would be the likely weight assigned to the fourth month?

The Weight catagory must equal 100 Therefore: 0.2+0.25+0.25 = 0.70 70-100=30 Therefore the answer is 0.3

An investment firm wants to invest money in buying a new office building. If the economy is strong the building will cost $8,500,000 with a 75% probability and $2,500,000 with 25% if the economy is weak. What is the expected value of the investment if the firm buys an office building?

The calculation is ($8,500,000 * .75) + ($2,500,000 * .25) = $7,000,000 The answer is: $7,000,000

An investment firm wants to invest money in buying a hotel. If the economy is strong the building will cost $8,500,000 with a 75% probability and $4,500,000 with 25% if the economy is weak. What is the expected value of the investment if the firm buys an office building?

The calculation used is =($8,500,000 * .75) + ($4,500,000 * .25) = $7,500,000.

Probability x Value = what?

The expected value of the alternative

Calculate duration estimates for the following situations: A construction manager received an estimate from a sub-contracted plumber for completion of the 2.5 bathrooms. The plumber thought it could be done in as few as 20 labor hours, although this type of design usually takes 28 hours. The plumber does remember that the last time, it took longer than usual and the labor hours climbed to 36. Using the beta distribution method, how many hours should the construction manager use as an estimate for the plumbing?

The formula is: Te = (o + 4m + p) / 6 28 hours

The beta distribution method is equal to the sum of the optimistic time estimate for the task (o), four times the most likely time (m) estimate, and the pessimistic time estimate (p); this result is then divided by six. What is the formla?

The formula is: Te=(o+4m+p)/6

Large Plant in a favorable market of 75% would cost $650 and an Unfavorable market of 25% it would cost $-100. If the company just got an updated forecast for the state of the future economy, and the likelihood of an unfavorable market increases to 35%, what will be the expected value for building a large plant?

The original equation was =(B1*0.75) + (C1*0.25) So, both probabilities for the conditions must be changed. The total probability for all conditions will equal 1. The new formula considering both probability changes will be =(B1•0.65) + (C1•0.35).

y = sqrt(x)+4 Is this equation linear or nonlinear and why.

The square root of x will result in a nonlinear equation. Only equations with x to the first power will result in a line.

Using the following sales data table, Month #1 the Weight was 0.2 and Sales were 600 Month #2 weight was 0.35 and sales 100 #3 weight 0.3 and sales 200 Month #4 weight was 0.15 and sales were 500 Calculate the moving average for the following four months of sales:

The unweighted average is the sum of all the sales. But the question is for the 'Weighted Average' Multiply each sales by its weight then add all values together. 120+35+60+75=290 The answer is 290

Find the median in the following list of numbers: 6, 4, 8, 10, 2, 5.

There are an even number of entries in the list, so add the two middle numbers and divide by 2 The median is 5.5

If 60 votes were cast. 40 men voted yes and 12 men voted no. 25 women voted yes and 13 voted no. What it the probabliity that a man voted yes?

Total of 60 votes and 40 men voted yes. 40/60 = 2/3 or 66.67%

Recall the steps necessary to calculate the standard deviation: 1. Calculate the mean of the data set. 2. Subtract the mean from each value in the data set. 3. Square each of the resulting deviations. 4. Add the squares of the deviations. 5. Divide by the number of values in the data set. (Note that if the data does not represent the entire population, but instead represents only a sample of the population, then divide by n-1 instead of n). 6. Calculate the non-negative square root of the result.

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