The variance of a sample of size n = 20 drawn from a normal population with mean 100 and variance 10 was obtained as s2 = 9.5.

(i) Determine the probability that S2 ≤ 10.

(ii) Determine the probability that S2 ≤ 9.5.

(iii) If the sample size increased by 50% but the computed sample variance remained the same, recompute the probability S2 ≤ 9.5.

(iv) Repeat part (iii) when the sample size is decreased from the original value of 50 by 50%.