4. A random sample of 15 strawberries is taken from a large field and the weight \(x\) grams of each strawberry is recorded. The results are summarised below.
$$\sum x = 291 \quad \sum x ^ { 2 } = 5968$$
Assume that the weights of strawberries are normally distributed. Calculate a 95\% confidence interval for
- the mean of the weights of the strawberries in the field,
- the variance of the weights of the strawberries in the field.
Strawberries weighing more than 23 g are considered to be less tasty.
- Use appropriate confidence limits from part (a) to find the highest estimate of the proportion of strawberries that are considered to be less tasty.