4 The lengths, \(x \mathrm {~m}\), of a random sample of 200 balls of string are found and the results are summarised by \(\Sigma x = 2005\) and \(\Sigma x ^ { 2 } = 20175\).
- Calculate unbiased estimates of the population mean and variance of the lengths.
- Use the values from part (i) to estimate the probability that the mean length of a random sample of 50 balls of string is less than 10 m .
- Explain whether or not it was necessary to use the Central Limit theorem in your calculation in part (ii).