- Jeremiah currently uses a Fruity model of juicer. He agrees to trial a new model of juicer, Zesty. The amounts of juice extracted, \(x \mathrm { ml }\), from each of 9 randomly selected oranges, using the Zesty are summarised as
$$\sum x = 468 \quad \sum x ^ { 2 } = 24560$$
Given that the amounts of juice extracted follow a normal distribution,
- calculate a 95\% confidence interval for
- the mean amount of juice extracted from an orange using the Zesty,
- the standard deviation of the amount of juice extracted from an orange using the Zesty.
Jeremiah knows that, for his Fruity, the mean amount of juice extracted from an orange is 38 ml and the standard deviation of juice extracted from an orange is 5 ml .
He decides that he will replace his Fruity with a Zesty if both
- the mean for the Zesty is more than \(20 \%\) higher than the mean for his Fruity and
- the standard deviation for the Zesty is less than 5.5 ml .
- Using your answers to part (a), explain whether or not Jeremiah should replace his Fruity with the Zesty.