6 In each of 38 randomly selected weeks of the English Premier Football League there were 10 matches. Table 1 summarises the number of home wins in 10 matches, \(X\), and the corresponding number of weeks. \begin{table}[h] \end{table} A researcher investigates whether \(X\) can be modelled by the distribution \(\mathrm { B } ( 10 , p )\). He calculates the expected frequencies using a value of \(p\) obtained from the sample mean.

1. Show that \(p = 0.45\). Table 2 shows the observed and expected number of weeks. \begin{table}[h]

   Number of home wins	0	1	2	3	4	5	6	7	8	9	10	Totals
   Observed number of weeks	0	1	2	8	8	9	7	1	2	0	0	38
   Expected number of weeks	0.096	0.788	2.899	6.326	9.058	8.893	6.064	2.835	0.870	0.158	0.013	38

   \captionsetup{labelformat=empty} \caption{Table 2
2. Show how the value of 2.835 for 7 home wins is obtained.}