- The stem and leaf diagram shows the number of deliveries made by Pat each day for 24 days
\begin{table}[h]
\captionsetup{labelformat=empty}
\caption{Key: 10 \(\mathbf { 8 }\) represents 108 deliveries}
| 10 | 8 | 9 | | | | | | | | | | (2) |
| 11 | 0 | 3 | 6 | 6 | 6 | 8 | 8 | 9 | 9 | 9 | 9 | (11) |
| 12 | 4 | 5 | 5 | 5 | 5 | 5 | 5 | 8 | | | | (8) |
| 13 | \(a\) | \(b\) | \(c\) | | | | | | | | | (3) |
\end{table}
where \(a\), \(b\) and \(c\) are positive integers with \(a < b < c\)
An outlier is defined as any value greater than \(1.5 \times\) interquartile range above the upper quartile.
Given that there is only one outlier for these data,
- show that \(c = 9\)
The number of deliveries made by Pat each day is represented by \(d\)
The data in the stem and leaf diagram are coded using
$$x = d - 125$$
and the following summary statistics are obtained
$$\sum x = - 96 \quad \text { and } \quad \sum ( x - \bar { x } ) ^ { 2 } = 1306$$ - Find the mean number of deliveries.
- Find the standard deviation of the number of deliveries.
One of these 24 days is selected at random. The random variable \(D\) represents the number of deliveries made by Pat on this day.
The random variable \(X = D - 125\)
- Find \(\mathrm { P } ( D > 118 \mid X < 0 )\)