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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 nn Fuchi apples, find the least nn 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.

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