1. TABLE 1 shows the total number of man-days lost to sickness during one

week’s operation of a small chemical plant. 

Showing all of your working, calculate the arithmetic mean and standard

deviation of the number of days lost.

2. The school of Science and Engineering at a local university regularly

purchases a particular type of electrical component. 60% are purchased

from company A, and 40 % are from Company B.

2% of those supplied by company A and 1% of those supplied by

Company B are known to be defective.

The components are identical and thoroughly mixed on receipt.

(a) Draw a tree diagram to represent the possible outcomes when a

single component is selected at random.

(b) A component is selected at random.

(i) What is the probability that this component was supplied by

company A and was defective?

(ii) Calculate the probability that the component was defective.

(iii) Given that the component was defective, what is the probability

that it was supplied by company A?

Length of metal strips produced by a machine are normally distributed

with mean length of 150 cm and a standard deviation of 10 cm.

Find the probability that the length of a randomly selected strip is

(a) Shorter than 165 cm.

(b) Longer than 170 cm.

(c) Between 145 cm and 155 cm.

4. The torque, T Nm, required to rotate shafts of different diameters, D mm,

on a machine has been tested and recorded below.

Plot a scatter diagram of the results with diameter of the machine as

the independent variable.

(b) Use the method of least squares to determine the linear regression

equation that relates the torque to the diameter.

(c) Estimate the value of torque required when the diameter is 16 mm.

(d) Calculate the coefficient of correlation between these variables and

comment on your prediction obtained in (c). 

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