Notes, summaries, assignments, exams, and problems for Mathematics

Gantt Charts and Project Status

Gantt charts are bar graphs that immediately show the status of implementation within a project, identifying any delays or advances. They attempt to represent the duration of each of the activities into which the project is divided. A drawback to their use is that they do not permit cross-connections showing directly how one activity depends on or influences another.

CPM / PERT Terminology Definitions

Activity

Each element of the project or program represented by an arc in CPM. This arc sometimes represents a time duration or a connection between two events of the graph. An activity cannot begin while the preceding event has not occurred.

Event

An event in the project or CPM that marks the beginning or end of an activity.... Continue reading "Understanding Gantt Charts and CPM/PERT Terminology" »

Exercise 01: Call Center Call Time

Suppose that the time needed for customer service calls in a telephone call center follows a Normal distribution with a mean of 8 minutes and a standard deviation of 2 minutes.

1. What is the probability that a call lasts less than five minutes?
2. What is the probability that a call lasts more than 9.5 minutes?
3. What is the probability that a call lasts between 7 and 10 minutes?
4. 75% of calls require at least how long for service?

Exercise 02: Rabbit Weight Classification

The distribution of the weights of rabbits raised on a farm may well be represented by a Normal distribution with a mean of 5 kg and a standard deviation of 0.9 kg. An abattoir buys 5000 rabbits and intends to classify them according to weight as follows:... Continue reading "Statistics Exercises: Normal Distribution" »

Core Concepts in Probability Distributions

Random Variables Defined

Random variables are those variables that assume different values as a result of a random experiment. They are classified into two main types:

• Discrete Random Variables: These support only integer values (countable outcomes).
• Continuous Random Variables: These support all types of values, including integers and fractions (measurable outcomes).

What is a Discrete Probability Distribution?

It is a theoretical frequency distribution, similar to relative frequencies. It maps the values of variables to the probability of occurrence of that value, representing what would be expected if the experiment were carried out repeatedly.

Key Discrete Probability Distributions

Binomial Distribution

Working Papers

These are the documents in which the auditor records the data and information obtained during their review, as well as the results of the tests performed.

Summary Warrant

A sample of major accounts that are an item.

Worksheet

This is the card that shows the groups or items that comprise the financial statements.

Decree of Detail

The items that comprise an account balance of a major account or any other account.

Certificates of Verification

The work performed to verify the correctness of an item or transaction.

Situations for Audit Work Plan

• Ensure that the service is clearly controlled.
• Be fully aware of what is being offered.

Conditions to Perform the Audit

• Maintain independence of mind regarding the specific client.
• Possess the ability to

Sampling Process and Principles

To ensure a sample accurately represents the population under investigation, its size and the methodology used must adhere to specific principles.

Core Sampling Concepts

Population (Universe)

The population, or universe, is defined as the complete set of elements existing within a specific space and time, all of which are affected by the same problem under study, and from which information is desired.

Sample

A sample is a representative fraction of the population. From the sample, we can infer or estimate the characteristics of the entire population.

Sampling

Sampling is the procedure for selecting a subset of elements (the sample) from a larger group (the population) in order to make inferences about the population.... Continue reading "Statistical Sampling: Core Concepts and Essential Elements" »

Balance Sheet: The second column in this column should note the value amount of each account. The third column space in this column records the total amount for each group. The fourth column in this column should write down the total amounts of the assets, liabilities, and stockholders' equity. Comparative balance sheet reporting shows that assets less liabilities equals capital employed. The first column should write down the amount of each of the accounts involved in the final. The second column is used to note the amount of each of the accounts up to the initial balance. The third column is used to assemble the alteration or difference of each account. The fourth column is used to denote the signs of plus or minus. Output states location... Continue reading "Understanding Balance Sheets and Income Statements" »

Types of Auditor Opinions

Unqualified Opinion

An unqualified opinion is issued when:

• The audit was performed without limitations in scope and in accordance with the National Technical Standards (NTA).
• The annual accounts have been prepared in accordance with accounting rules and Generally Accepted Accounting Principles (GAAP), consistent with prior years.
• The information, including supporting documentation, is sufficient for adequate comprehension.
• The financial statements, taken as a whole, fairly represent the company's business in accordance with the information available to the auditor.

Qualified Opinion

A qualified opinion is issued when the auditor concludes that there are significant circumstances that prevent the annual accounts from presenting... Continue reading "Auditor's Opinions: Types and Implications" »

 Where are logged grocery outlets? 

 A: At the request of warehouse and should be downloaded from the stock sheets of each product grocery or warehouse management system. 

 Where recorded outputs of meat? 

 A: At the request of warehouse and should be downloaded from the stock form of meat or warehouse management system 

 How do you record the output of fruits and vegetables? 

 A: At the request of warehouse and should be downloaded from the stock card for each item of fruit and vegetables or warehouse management system. 

 How losses are recorded? 

 R: We recorded in a control sheet shrinkage, which is used in the areas of prepackaged and in each production area, respectively. 

 Should there be a requisition order (order form only for the entire restaurant?

Methodology Steps for Analysis

The following steps outline a process for analyzing data, likely related to quality or process issues:

1. Establish a list of reasons.
2. Appreciate the importance of each cause.
3. Calculate the percentage ratings.
4. Classify as growing percentages obtained.
5. Rendering a column chart.
6. Plotting the graph of the cumulative values (Dickey curve).
7. Determine areas A, B, and C.

5. Estratificación (Stratification)

What is it? Why?

Stratifying the data collected involves subdividing it into a number of homogeneous groups to facilitate understanding and analysis of the phenomenon under study. The goal is to define the factor or factors most significant in terms of data representing the phenomenon.

Stratification should be used in the approach... Continue reading "Data Analysis Techniques: Stratification and Cause-Effect Diagrams" »

Constant Force Micrometer Mechanisms

Figure 3.34 illustrates a constant force mechanism designed to ensure measurements remain unaffected by variations in pressure. This system utilizes two constant force components to maintain measurement consistency.

Metric Micrometer Measurements

The thread pitch is 0.5 mm, meaning a full turn of the screw increases or decreases the distance between the measuring stops by 0.5 mm. The graduations on the sleeve above the reference line represent millimeters, while those below represent half-millimeters, corresponding to the spindle's movement. To achieve an accuracy of 0.01 mm, the drum scale must contain 50 divisions.

Reading a Metric Micrometer

To obtain a reading, follow these steps:

• Note the last number visible