5 The 150 oranges in a random sample from a certain supplier were weighed and the masses, \(X\) grams, were recorded. The results are summarised below.
$$n = 150 \quad \Sigma x = 14910 \quad \Sigma x ^ { 2 } = 1525000$$
- Calculate a \(99 \%\) confidence interval for the population mean of \(X\).
- The supplier claims that the mean mass of his oranges is 100 grams. Use your answer to part (i) to explain whether this claim should be accepted.
- State briefly why the sample should be random.