We can also use RStudio to calculate quantiles for the normal distribution, that is, values such that the area under the curve to the left equals a pre-specified value. Work through: . Section 5.4 - Calculating quantiles for the standard normal distribution, and calculating quantiles for any normal distribution. Answer the following questions: 1. If Z is the standard normal distribution, use RStudio to find (correct to at least two decimal places) the value of z such that: 35 % of observations fall below z = 55 % of observations fall below z = TIP! If the question says correct to at least x significant figures or If the question says correct to at least y decimal places, do not bother rounding, just copy and paste what RStudio gives you. It avoids the risk of making a mistake when rounding and it avoids the risk of making a mistake when retyping the numbers. Exams question almost always say "at least" so this is a good tip! The question below is there just to ensure you know what significant figures and decimal places are. 2. If X follows a standard normal distribution with mean 15 and standard deviation 2.5 (this can be written as X ~ N(15, 2.5 ), use RStudio to find q such that P(X > q) = 0.21: (you will enter your answer twice below, paying close attention to the instructions. The goal is to incorporate revisions of decimal places vs significant figures before the final exam) q = (correct to exactly two decimal places) q = (correct to exactly two significant figures) 3. If the annual return expressed as a percentage from the All Ordinaries Index is approximately distributed as X ~ N(11.1, 10), use RStudio to find a value (correct to at least two decimal places) which we expect the annual return to exceed only once every four years (the probability of getting less than that return is 0.75)