A sample of 50 washed baking potatoes was selected at random from a large batch.
The weights of the 50 potatoes were found to have a mean of 234 grams and a standard deviation of 25.1 grams.
Construct a \(95 \%\) confidence interval for the mean weight of potatoes in the batch.
(4 marks)
The batch of potatoes is purchased by a market stallholder. He sells them to his customers by allowing them to choose any 5 potatoes for \(\pounds 1\).
Give a reason why such chosen potatoes are unlikely to represent a random sample from the batch.