Chapter 16, Probability and Statistics Video Solutions, Engineering Mathematics Through Applications

Problem 1

State whether the following are discrete
or continuous data:
c The number of motors in a batch
a The weights of people
d The lifetimes of light bulbs
b Marks in an examination
e The resistance value of a variable resistor.

Rashmi Sinha

Numerade Educator

02:00

Problem 2

The temperatures, to the nearest degree Celsius, for the last 30 days are as follows:
$\begin{array}{llllll}22 & 23 & 23 & 16 & 17 & 20 \\ 21 & 24 & 18 & 17 & 19 & 21 \\ 23 & 25 & 26 & 21 & 20 & 20 \\ 16 & 15 & 17 & 22 & 24 & 23 \\ 23 & 19 & 20 & 22 & 21 & 20\end{array}$
Construct a frequency distribution.

James Kiss

Numerade Educator

01:40

Problem 3

The heights, in $\mathrm{m}$, of 40 students are shown below:
$\begin{array}{llllllll}1.68 & 1.67 & 1.53 & 1.70 & 1.69 & 1.71 & 1.71 & 1.80 \\ 1.81 & 1.85 & 1.76 & 1.66 & 1.91 & 1.95 & 1.87 & 1.80 \\ 1.82 & 1.76 & 1.84 & 1.55 & 1.61 & 1.85 & 1.93 & 1.88 \\ 1.95 & 1.57 & 1.97 & 1.56 & 1.99 & 1.83 & 1.74 & 1.83 \\ 1.86 & 1.88 & 1.93 & 1.64 & 1.89 & 1.90 & 1.72 & 1.95\end{array}$
Construct a frequency distribution with an equal class width of $0.1$.

Nidhi Singhi

Numerade Educator

01:02

Problem 4

Draw a histogram for question 3 with the same class width.

Abhishek Kumar

Numerade Educator

01:50

Problem 5

Draw a frequency polygon for question $3 .$

Julian Wong

Numerade Educator

01:06

Problem 6

The table below shows the time taken, in ms, for 105 op-amps to become fully operational:
$$
\begin{array}{|c|c|}
\hline \text { Time taken } t(\mathrm{~ms}) & \text { Frequency } \\
\hline 10 \leq t<20 & 10 \\
20 \leq t<30 & 14 \\
30 \leq t<40 & 18 \\
40 \leq t<45 & 16 \\
45 \leq t<50 & 12 \\
50 \leq t<55 & 8 \\
55 \leq t<70 & 15 \\
70 \leq t<100 & 12 \\
\hline
\end{array}
$$
Draw a histogram to illustrate this data.

Carson Merrill

Numerade Educator

03:26

Problem 7

The following table shows the lifetime (in hours) of 88 light bulbs:
$$
\begin{array}{l|c|}
\hline \text { Lifetime } L \text { (hours) } & \text { Frequency } \\
\hline 150 \leq L<200 & 5 \\
200 \leq L<250 & 7 \\
250 \leq L<300 & 10 \\
300 \leq L<350 & 12 \\
350 \leq L<400 & 14 \\
400 \leq L<450 & 11 \\
450 \leq L<500 & 10 \\
500 \leq L<550 & 8 \\
550 \leq L<600 & 7 \\
\hline 600 \leq L<650 & 4 \\
\hline
\end{array}
$$
Draw a frequency polygon to illustrate, this data.

John Long

Numerade Educator

02:16

Problem 8

The diameter of 100 piston rings are measured and recorded as follows:
$$
\begin{array}{|c|c|}
\hline \text { Diameter } d(\mathrm{~mm}) & \text { Frequency } \\
\hline 86.00 \leq d<86.10 & 9 \\
86.10 \leq d<86.15 & 9 \\
86.15 \leq d<86.25 & 12 \\
86.25 \leq d<86.40 & 15 \\
86.40 \leq d<86.45 & 10 \\
86.45 \leq d<86.50 & 7 \\
86.50 \leq d<86.70 & 20 \\
86.70 \leq d<87.00 & 18 \\
\hline
\end{array}
$$
Draw a histogram and a frequency polygon for this data.

Hast Aggarwal

Numerade Educator

00:39

Problem 9

The table to the right shows the number of new registrations with the Engineering Council at the end of each year. Draw a vertical bar chart to represent the number of registrations of CEng, IEng and EngTech against each year on the same graph.

Comment on your graph and data.

Hossam Mohamed

Numerade Educator