Higher Engineering Mathematics, Sixth Edition

Revision Test 16

This Revision Test covers the material contained in Chapters 54 to 56.The marks for each question are shown in
brackets at the end of each question.

1. A company produces five products in the following
   proportions:

Product A 24 Product B 16 Product C 15

Product D 11 Product E 6

Present these data visually by drawing (a) a vertical

bar chart, (b) a percentage component bar chart,

(c) a pie diagram. (13)

2. The followinglists the diameters of 40 components
   produced by a machine, each measured correct to
   the nearest hundredth of a centimetre:
   1.39 1.36 1.38 1.31 1.33 1.40 1.28
   1.40 1.24 1.28 1.42 1.34 1.43 1.35
   1.36 1.36 1.35 1.45 1.29 1.39 1.38
   1.38 1.35 1.42 1.30 1.26 1.37 1.33
   1.37 1.34 1.34 1.32 1.33 1.30 1.38
   1.41 1.35 1.38 1.27 1.37

(a) Using 8 classes form a frequency distribution

and a cumulative frequency distribution.

(b) For the above data draw a histogram, a fre-

quency polygon and an ogive. (21)

3. Determine for the 10 measurements of lengths
   shown below:
   (a) the arithmetic mean, (b) the median, (c) the
   mode, and (d) the standard deviation.
   28m, 20m, 32m, 44m, 28m, 30m, 30m, 26m,
   28m and 34m (10)


4. The heights of 100 people are measured correct to
   the nearest centimetre with the following results:
   150–157cm 5 158–165cm 18
   166–173cm 42 174–181cm 27
   182–189cm 8

Determine for the data (a) the mean height and

(b) the standard deviation. (12)

5. Draw an ogive for the data of component mea-
   surements given below, and hence determine the
   median and the first and third quartile values for
   this distribution.

Class Frequency Cumulative

intervals (mm) frequency

1.24–1.26 2 2

1.27–1.29 4 6

1.30–1.32 4 10

1.33–1.35 10 20

1.36–1.38 11 31

1.39–1.41 5 36

1.42–1.44 3 39

1.45–1.47 1 40

(10)

6. Determine the probabilities of:
   (a) drawing a white ball from a bag containing
   6 black and 14 white balls,
   (b) winning a prize in a raffle by buying 6 tickets
   when a total of 480 tickets are sold,
   (c) selecting at random a female from a group of
   12 boys and 28 girls,
   (d) winning a prize in a raffle by buying 8 tickets
   whenthereare5prizesandatotalof800tickets
   are sold. (8)


7. The probabilities of an engine failing are given by:
   p 1 , failure due to overheating;p 2 , failure due to
   ignitionproblems;p 3 , failure due to fuel blockage.
   Whenp 1 =

1

8

, p 2 =

1

5

andp 3 =

2

7

, determine the

probabilities of:

(a) all three failures occurring,

(b) the first and second but not the third failure

occurring,

(c) only the second failure occurring,

(d) the first or the second failure occurring but not

the third. (12)

8. In a box containing 120 similar transistors 70 are
   satisfactory, 37 give too high a gain under normal