Task 5

In this task, you will be able to apply statistical techniques to engineering problems.

Scenario: Statistical techniques are commonly used to study the engineering problems such as material testing, quality control etc. Engineering problems with different discrete and continuous distribution are stated in this task to illustrate the practical use of statistical techniques mentioned in the course.

Task 5.1 (P5.1)

a) The points with coordinates (0, 6), (2, 7), (4, 8) and (6, 9) lie on a straight line.

Draw the line and determine its equation.

b) The following graph shows a scatter plot and a line of best fit:

Determine the equation of the line of best fit.

Use the equation to estimate y when x = 4.

Use the equation to estimate x when y = 18

Task 5.2 (P5.2)

Analyse the probability distributions for discrete and continuous data with the following situations.

Concrete blocks are tested and it is found that, on average, 7% fail to meet the required specification. For a batch of 9 blocks, determine the probabilities that less than three blocks will fail to meet the specification. This is to determine the distributions for discrete or continuous data, please explain it.

Task 5.3 (P5.3)

A package contains 50 similar components and inspection shows that 4 have been damaged during transit. If 6 components are drawn at random from the contents of the package determine the probabilities that in this sample a) one and b) less than 2 are damaged.