A hint to get started
Combine normal observations and choose a minimum sample size
The mass of a Munchi pear is normally distributed with mean 120 g and standard deviation 10 g.
(i) Two pears are chosen at random. Find the probability that one has mass between 100 g and 126 g while the other has mass greater than 130 g.
(ii) Ten pears are chosen at random. Find the probability that exactly three have mass greater than 122 g each.
The mass of a Fuchi apple is normally distributed with mean 115 g and standard deviation 8 g.
(iii) Find the probability that the total mass of three randomly chosen Fuchi apples exceeds three times the mass of one randomly chosen Munchi pear.
(iv) For a random sample of Fuchi apples, find the least such that the probability that its sample mean differs from 115 g by more than 4 g is not more than 0.3.
[2010/NYJC/II/12]
CJC · Discussion · Question 4
Track whether a variable is summed independently or multiplied as a single observation.