Higher Engineering Mathematics

Assign-15-H8152.tex 23/6/2006 15: 14 Page 551

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Statistics and probability

Assignment 15

This assignment 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 follow-
   ing proportions:

Product A 24 Product B 16 Product C 15

Product D 11 Product E 6

Present these data visually by drawing (a) a verti-

cal bar chart (b) a percentage component bar chart

(c) a pie diagram. (13)

2. The following lists the diameters of 40 compo-
   nents 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

frequency 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.
   28 m, 20 m, 32 m, 44 m, 28 m, 30 m, 30 m, 26 m,
   28 m and 34 m (10)


4. The heights of 100 people are measured correct to
   the nearest centimetre with the following results:

150–157 cm 5 158–165 cm 18

166–173 cm 42 174–181 cm 27

182–189 cm 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

when there are 5 prizes and a total of 800

tickets are sold. (8)

7. The probabilities of an engine failing are given
   by:p 1 , failure due to overheating;p 2 , failure due
   to ignition problems;p 3 , failure due to fuel block-

age. 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