7. The times taken by a large number of people to read a certain book can be modelled by a normal distribution with mean \(5 \cdot 2\) hours. It is found that \(62 \cdot 5 \%\) of the people took more than \(4 \cdot 5\) hours to read the book.

1. Show that the standard deviation of the times is approximately \(2 \cdot 2\) hours.
2. Calculate the percentage of the people who took between 4 and 7 hours to read the book.
3. Calculate the probability that two of the people chosen at random both took less than 5 hours to read the book, stating any assumption that you make.
4. If a number of extra people were taken into account, all of whom took exactly \(5 \cdot 2\) hours to read the book, state with reasons what would happen to (i) the mean, (ii) the variance and explain briefly why the distribution would no longer be normal.