Answer all questions in this section (40 marks in total). 1. Give brief answers to each of the following questions. (a) Maria has an important job interview in the morning. To ensure she wakes up in time, she sets two alarm clocks which ring with probabilities 0.97 and 0.99 respectively. What is the probability that at least one of the alarm clocks will wake her up? (b) Suppose that the distribution of a set of values has a population mean of 50 and a population variance of 6. If 4 is subtracted from each score and then each score is divided by 2, what will be the new mean and variance of the set of values? (c) If X ~ Bin(n,7r) state, in terms of n and 7t, what the approximating Poisson and Normal distributions would be. (d) State the Central Limit Theorem. (e) When and why can a standard normal distribution be used to approximate a Student's t distribution? (t) In a hypothesis test for a single proportion using a normal distribution, we have H0 : 7r = 0.7 and H1 : 7r