Question 5(7 points)

Apple Of My IsleOrchardsis harvesting apples to send to market. Different qualities of apple can be sold for a different price, so it is important to accurately sort the apples.

Apple size follows a normal distribution which is assumed to have mean 90gm and standard deviation 12gm. Apples moving down a conveyor belt must be visually checked to see if they are undersize, midsized, or large. The size cut offs are

<70gm

undersize

>105gm

large

Otherwise

midsized

1. [3 marks] What proportion of apples are expected to be undersize, mid-sized or large? Show your working either by giving a z-score or by giving the EXCEL formula you used to perform the calculation.
2. [2 marks] If the mean weight of apples was 85gm instead of 90gm how you expect the proportion of undersize, midsize and large apples to change?
3. [1 mark] If the standard deviation increased from 12gm to 15gm would you expect the proportion of mid-sized apples to increase or decrease?
4. [1 mark] Assuming that the apples are well mixed, if you have a run of 10 large apples in a row is it more likely that the next apple you sort will be medium sized or smaller?