The diameter of an orange is normally distributed with mean 7cm and standard deviation 1cm. Using a series of sieves, we wish to sort the oranges into three classes. Class 1 should contain large oranges, class 2 should contain medium oranges, and class 3 should contain small oranges in the proportion of 20%, 50%, and 30%.
Please see the attached image.
Q1) How should we choose the gaps d1 and d2?
Q2) If the gaps are appropriately choses, what is the probability that out of 10 oranges, 6 or more oranges fall into class 2?