Q4. (a) Discuss all possible shapes of normal distribution. How is the shape of a normal distribution obtained? [4]

(b) Why is standard normal random variable used instead of normal random variable.

Define central limit theorem (CLT). How is CLT associated with normal distribution? [6]

(c) Students in ACT2105 spend on average 3.9 hours a week studying (with a

population standard deviation = 5). Given this fact, describe the sampling

distribution of the mean if all possible random samples of size 50 were chosen.

What can you say about the mean of all the possible sample means?