Probability Simulations and Statistical Analysis using R Programming
Repeat 1000 times the experiment you performed in Task 1, that is rolling a tetrahedron die 10 times and computing the average. Report the average and standard deviation of the 1000 experiments. The standard deviation function in R is sd(x).
S = 1000
rolls.Avgs = vector(length = S)
for(simnum in 1:S){
x = 1:4
roll = sample(x, 10, replace = TRUE)
rolls.Avgs[simnum] = mean(roll)
}
mean(rolls.Avgs)
sd(rolls.Avgs)
# compute the mean of the 1000 experiments
mean(rolls.Avgs)
hist(rolls.Avgs, main=””, xlab=
Essential Geometry Terms and Definitions Glossary
A
Acute Angle
An angle measuring less than 90°.
Acute Triangle
A triangle where all three interior angles are acute (less than 90°).
Altitude of a Triangle
A perpendicular segment from a vertex to the opposite side or to a line containing the opposite side.
Angle
It is formed by two rays that share a common endpoint, provided that the two rays are noncollinear.
Angle Bisector
A ray that contains the vertex and divides the angle into two congruent angles.
Arc
Two points on the circle and a continuous part
Read MoreEssential Geometry Concepts: Formulas, Proofs, and Theorems
Fundamentals of Geometry
Undefined Terms and Basic Figures
- Point: Exact location in space with no size, written as a capital letter (e.g., A).
- Line: Straight path extending infinitely in both directions, no thickness, named with two points ($\overleftrightarrow{AB}$) or a lowercase script letter.
- Plane: Flat surface extending infinitely in all directions, named with a script capital letter or three non-collinear points.
- Collinear Points: Points that lie on the same line.
- Coplanar Points: Points that lie
Quality Management Calculations: EPMO, Control Charts, and Capability
Problem #6-1:
A bank has set a Standard that mortgage applications be processed within a certain number of days Of filing. If, out of a sample of 1000 Applications, 75 fail to meet this requirement, what is the epmo metric?
75 errors per Thousand is equivalent to 75000 epmo.
Problem #6-2:
Over the last year, 965 injections were administered at a clinic. Quality is measured by the proper amount of dosage as well as the Correct drug. In two instances, the Incorrect amount was given, and
Read MoreEssential Quality Tools for Process Improvement and Analysis
Quality Tools for Process Control
Quality tools are essential instruments used to control a process, identify faults, improve risk analysis systems, and drive continuous improvement.
Brainstorming
Brainstorming is a technique where a group encourages every member to participate and generate ideas, focusing on quantity over complexity. It is crucial that the group avoids criticizing ideas during the generation phase, as only some ideas will ultimately be valid.
Requirements for Effective Brainstorming
- The
Business Profitability: Revenue, Costs, and Break-Even Analysis
Understanding Business Profitability
Profit is the essential difference between a business’s revenue (sales) and its costs. When x units are produced and sold, this relationship can be expressed mathematically:
P(x) = R(x) - C(x)
Profit Calculation Fundamentals
Where:
- P(x): Represents the total profit derived from the sale of x units.
- R(x): Represents the total revenue generated from the sale of x units.
- C(x): Represents the total cost associated with the production and sale of x units.