ABSTRACT
This Revision Test covers the material in Chapters 37 to 39. The marks for each question are shown in brackets at the end of each question.
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 bar chart, (c) a pie diagram. (13)
The following lists 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 $$ \begin{aligned}\begin{array}{lllllll} 1.39&1.36&1.38&1.31&1.33&1.40&1.28\\ 1.40&1.24&1.28&1.42&1.34&1.43&1.35\\ 1.36&1.36&1.35&1.45&1.29&1.39&1.38\\ 1.38&1.35&1.42&1.30&1.26&1.37&1.33\\ 1.37&1.34&1.34&1.32&1.33&1.30&1.38\\ 1.41&1.35&1.38&1.27&1.37&\,&\end{array}\end{aligned} $$ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315561851/68dfa506-c5cb-44dc-acc2-051e8137b6fd/content/mathrev10um_1.tif"/>
Using 8 classes form a frequency distribution and a cumulative frequency distribution
For the above data draw a histogram, a frequency polygon and an ogive (21)
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 (9)
The heights of 100 people are measured correct to the nearest centimetre with the following results: 150 - - 157 c m 5 158 - - 165 c m 18 166 - - 173 c m 42 174 - - 181 c m 27 182 - - 189 c m 8 $$ \begin{aligned}\begin{array}{llll} 150--157\,cm&5&158--165\,cm&18\\ 166--173\,cm&42&174--181\,cm&27\\ 182--189\,cm&8&\,&\end{array}\end{aligned} $$ https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781315561851/68dfa506-c5cb-44dc-acc2-051e8137b6fd/content/mathrev10um_2.tif"/> Determine for the data (a) the mean height and (b) the standard deviation. (10)
Determine the probabilities of:
drawing a white ball from a bag containing 6 black and 14 white balls
winning a prize in a raffle by buying 6 tickets when a total of 480 tickets are sold
selecting at random a female from a group of 12 boys and 28 girls
winning a prize in a raffle by buying 8 tickets when there are 5 prizes and a total of 800 tickets are sold (8)
In a box containing 120 similar transistors 70 are satisfactory, 37 give too high a gain under normal operating conditions and the remainder give too low a gain. Calculate the probability that when drawing two transistors in turn, at random, with replacement, of having (a) two satisfactory, (b) none with low gain, (c) one with high gain and one satisfactory, (d) one with low gain and none satisfactory. Determine the probabilities in (a), (b) and (c) above if the transistors are drawn without replacement. (14)
