The random variable \(X\) has the discrete uniform distribution and takes the values \(\{ 1 , \ldots , n \}\). The standard deviation of of \(X\) is \(2 \sqrt { 6 }\). Find
the mean of \(X\),
\(\mathrm { P } \left( 3 \leq X < \frac { 1 } { 2 } n \right)\).
The rainfall at a weather station was recorded every day of the twentieth century. One year is selected at random from the records and the total rainfall, in cm , in January of that year is denoted by \(R\) Assuming that \(R\) can be modelled by a normal distribution with standard deviation \(12 \cdot 6\), and given that \(\mathrm { P } ( R > 100 ) = 0 \cdot 0764\),
find the mean of \(R\),
calculate \(\mathrm { P } ( 75 < R < 80 )\).
The length of time, in minutes, that visitors queued for a tourist attraction is given by the following table, where, for example, ' 20 - ' means from 20 up to but not including 30 minutes.
Queuing time (mins)
\(0 -\)
\(10 -\)
\(15 -\)
\(20 -\)
\(30 -\)
\(40 - 60\)
Number of visitors
15
24
\(x\)
13
10
\(y\)
State the upper class boundary of the first class.
A histogram is drawn to represent this data. The total area under the histogram is \(36 \mathrm {~cm} ^ { 2 }\). The ' 10 - ' bar has width 1 cm and height 9.6 cm . The ' 15 - ' bar is ten times as high as the '40-60' bar.
Find the values of \(x\) and \(y\).
On graph paper, construct the histogram accurately.