Statistics
Mathematics Worked Examples by Topics
| Number | Mathematical Skills | Applications |
|---|---|---|
| 1 | Number, percentages, and percentiles | Determining the amounts, costs, and dimensions of materials |
| 2 | Ratio | Scaling models, dimensions, shapes, and drawings |
| 3 | Surface area/Volume | Finding costs of quantities, waste amounts |
| 4 | Trigonometry | Calculating angles/lengths of products |
| 5 | Graphs and charts | Using data to make decisions/visualization of data |
| 6 | Coordinates and geometry | Using coordinates for design drawings |
| 7 | Statistics | Using data to make informed design decisions |
Statistics
Question 1)
A student is cutting out a piece of wood for his design project. To do this his needs to use the bandsaw. The probability that the bandsaw is free is 0.65. The probability that the PPE he needs for bandsaw is free is 0.35. Calculate the probability that he can undertake his work.
Step 1) Calculate the probability:
Probability = 0.65 x 0.35 = 0.2275
Question 2)
The manufacturer of engine has three quality control checks to perform. Given that 50,000 parts are made in a day. How many parts fail in a working week (5 days). A part fails the quality control check if all 3 tests fail together.
- Probability of test A failing = 0.01
- Probability of test B failing = 0.03
- Probability of test C failing = 0.05
Step 1) Calculate the probability of a part failing all 3 tests:
Probability of all 3 failing = 0.01 x 0.03 x 0.05 = 0.000015
Step 2) Calculate the number of parts that fail in a day
Daily failures = 50,000 x 0.000015 = 0.75
Step 3) Calculate the number of parts that fail in a working week:
Failures in a week = 0.75 x 5 = 3.75 parts
Question 3)
The probability any student fails there DT exam 0.05, if 3 students fail within a class the DT teacher will get sacked. In a class of 50 is it expected that the teacher will get sacked?
Step 1) Calculate the number of students likely to fail:
Probability = 0.05 x 50 = 2.5 students fail (i.e. the teacher is likely not to get sacked)
Question 4)
Following on from question 3, how many more students are needed in the class before it is likely the teacher will be sacked
Step 1) Calculate the number of students needed until 3 fail:
3 Fails = x (number of students in class) x 0.05
Step 2) Solve for x (number of students in class):
x = 3⁄0.05 = 60 students
So an extra 10 students are needed