A random sample \(X _ { 1 } , X _ { 2 } , \ldots , X _ { 10 }\) is taken from a normal population with mean 100 and standard deviation 14.
Write down the distribution of \(\bar { X }\), the mean of this sample.
Find \(\mathrm { P } ( | \bar { X } - 100 | > 5 )\).
A random sample of the invoices, for books purchased by the customers of a large bookshop, was classified by book cover (hardback, paperback) and type of book (novel, textbook, general interest). As part of the analysis of these invoices, an approximate \(\chi ^ { 2 }\) statistic was calculated and found to be 11.09 .
Assuming that there was no need to amalgamate any of the classifications, carry out an appropriate test to determine whether or not there was any association between book cover and type of book. State your hypotheses clearly and use a \(5 \%\) level of significance.
(6 marks)