7 Rose and Emma each wear a device that records the number of steps they take in a day. All the results for a 7-day period are given in Fig. 7.
\begin{table}[h]
| Day | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| Rose | 10014 | 11262 | 10149 | 9361 | 9708 | 9921 | 10369 |
| Emma | 9204 | 9913 | 8741 | 10015 | 10261 | 7391 | 10856 |
\captionsetup{labelformat=empty}
\caption{Fig. 7}
\end{table}
The 7-day mean is the mean number of steps taken in the last 7 days. The 7-day mean for Rose is 10112 .
- Calculate the 7-day mean for Emma.
At the end of day 8 a new 7-day mean is calculated by including the number of steps taken on day 8 and omitting the number of steps taken on day 1 . On day 8 Rose takes 10259 steps.
- Determine the number of steps Emma must take on day 8 so that her 7 -day mean at the end of day 8 is the same as for Rose.
In fact, over a long period of time, the mean of the number of steps per day that Emma takes is 10341 and the standard deviation is 948.
- Determine whether the number of steps Emma needs to take on day 8 so that her 7 -day mean is the same as that for Rose in part (ii) is unusually high.