4. Kylie regularly travels from home to visit a friend. On 10 randomly selected occasions the journey time \(x\) minutes was recorded. The results are summarised as follows.
$$\Sigma x = 753 , \quad \Sigma x ^ { 2 } = 57455 .$$
- Calculate unbiased estimates of the mean and the variance of the population of journey times.
After many journeys, a random sample of 100 journeys gave a mean of 74.8 minutes and a variance of 84.6 minutes \({ } ^ { 2 }\).
- Calculate a 95\% confidence interval for the mean of the population of journey times.
- Write down two assumptions you made in part (b).