Higher Engineering Mathematics

Assign-16-H8152.tex 23/6/2006 15: 15 Page 576

Statistics and probability

Assignment 16

This assignment covers the material contained

in chapters 57 to 60.

The marks for each question are shown in

brackets at the end of each question.

1. A machine produces 15% defective components.
   In a sample of 5, drawn at random, calculate,
   using the binomial distribution, the probability
   that:
   (a) there will be 4 defective items
   (b) there will be not more than 3 defective items
   (c) all the items will be non-defective

Draw a histogram showing the probabilities of

0, 1, 2,..., 5 defective items. (20)

2. 2% of the light bulbs produced by a company are
   defective. Determine, using the Poisson distribu-
   tion, the probability that in a sample of 80 bulbs:
   (a) 3 bulbs will be defective, (b) not more than
   3 bulbs will be defective, (c) at least 2 bulbs will
   be defective. (13)


3. Some engineering components have a mean
   length of 20 mm and a standard deviation of
   0.25 mm. Assume that the data on the lengths
   of the components is normally distributed.

In a batch of 500 components, determine the

number of components likely to:

(a) have a length of less than 19.95 mm

(b) be between 19.95 mm and 20.15 mm

(c) be longer than 20.54 mm (15)

4. In a factory, cans are packed with an average of
   1.0 kg of a compound and the masses are nor-
   mally distributed about the average value. The
   standard deviation of a sample of the contents
   of the cans is 12 g. Determine the percentage of

cans containing (a) less than 985 g (b) more than

1030 g (c) between 985 g and 1030 g. (10)

5. The data given below gives the experimental val-
   ues obtained for the torque output,X, from an
   electric motor and the current,Y, taken from the
   supply.

TorqueX CurrentY

03

15

26

36

49

511

612

712

814

913

Determine the linear coefficient of correlation

for this data. (18)

6. Some results obtained from a tensile test on a
   steel specimen are shown below:

Tensile force (kN) Extension (mm)

4.8 3.5

9.3 8.2

12.8 10.1

17.7 15.6

21.6 18.4

26.0 20.8

Assuming a linear relationship:

(a) determine the equation of the regression line

of extension on force

(b) determine the equation of the regression line

of force on extension

(c) estimate (i) the value of extension when the

force is 16 kN, and (ii) the value of force

when the extension is 17 mm. (24)