Higher Engineering Mathematics, Sixth Edition

Revision Test 17

This Revision Test 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 willbe not more than 3 defective items,

(c) all the items will be non-defective.

Draw a histogram showing the probabilitiesof 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 20mm and a standard deviation of 0.25mm.
   Assume that the data on the lengths of the com-
   ponents is normally distributed.

In a batch of 500 components, determine the

number of components likely to:

(a) have a length of less than 19.95mm,

(b) be between 19.95mm and 20.15mm,

(c) be longer than 20.54mm. (15)

4. In a factory, cans are packed with an average of
   1.0kg of a compound and the masses are normally
   distributed about the average value. The standard
   deviation of a sample of the contents of the cans
   is 12g. Determine the percentage of cans con-
   taining (a) less than 985g, (b) more than 1030g,
   (c) between 985g and 1030g. (10)


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

TorqueX CurrentY

0 3

1 5

2 6

3 6

4 9

5 11

6 12

7 12

8 14

9 13

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 16kN, and (ii) the value of force

when the extension is 17mm. (24)