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Q2. (a) Explain in details and your own words what is a z-value and what property of a Normal Distribution can be derived from the Standard Normal Distribution (2) table. Grades will be awarded for correct and clear explanation of the process using terminologies used in this course. (b) Assuming that households' expenditure on Christmas presents in the UK is normally distributed with a mean of £580 and a standard deviation of £100, Calculate the probability that: (i) a randomly selected household spends less than £350. (ii) a randomly selected household spends between £400 and £700. (c) Explain in detail the application of continuity correction factor when Normal distribution is used to approximate binomial probabilities. Question 2 continues on the next page... 2 (d) A binomial probability distribution has 84 trials, with a probability of success of p = 0.70: (1) Calculate the mean and standard deviation. (ii) Find the probability of P(50 X 64) by applying the continuity correction factor and using normal approximation method. Show all your calculations.