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Question (a) Consider a random sample of the following data: 254, 261, 250, 258, 253, 257. Calculate the...

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(a) Consider a random sample of the following data: 254, 261, 250,258, 253, 257.
Calculate the unbiased estimator of the populationvariance.

(b) Suppose the GPA of all students enrolled in a particularcourse can be modelled by a
certain distribution with a mean of 3.4 and variance 0.3. Computethe probability that the
mean GPA of a random sample of 40 students selected from thiscourse will be:

(i) lower than 3.2
(ii) between 3.3 and 3.6


(c) Suppose you throw a die 600 times. Apply a suitable techniqueto compute the
approximate probability of obtaining between 90 and 110fours.

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