2 The weight, \(X\) grams, of a particular variety of orange is normally distributed with mean 205 and standard deviation 25.
- Determine the probability that the weight of an orange is:
- less than 250 grams;
- between 200 grams and 250 grams.
- A wholesaler decides to grade such oranges by weight. He decides that the smallest 30 per cent should be graded as small, the largest 20 per cent graded as large, and the remainder graded as medium.
Determine, to one decimal place, the maximum weight of an orange graded as:
- small;
- medium.
- The weight, \(Y\) grams, of a second variety of orange is normally distributed with mean 175.
Given that 90 per cent of these oranges weigh less than 200 grams, calculate the standard deviation of their weights.
(4 marks)