1. Given a random sample of 10 observations drawn from a Gaussian population with mean 100, and variance 25, compute the following probabilities regarding the sample mean, X¯:

(i) P (X¯  ≥ 100);

(ii) P (X¯  ≤ 100);

(iii) P (X¯  ≥ 104.5);

(iv) P (96.9 ≤ X¯ ≤ 103.1);

(v) P (98.4 ≤ X¯   ≤ 101.6).

Will the sample size make a di?erence in the distribution used to compute the probabilities?

2. Refer to Exercise 13.14. This time, the population variance is not given; instead, the sample variance was obtained as 24.7 from the 10 observations.

(i) Compute the ?ve probabilities.

(ii) Recompute the probabilities if the sample size increased to 30 but the sample variance remained the same.