5 3339 points Recall that in the construction of a boxplot a

5. [3+3+3=9 points] Recall that in the construction of a boxplot, any data falling below Q1 - 1.5 IQR or above Q3 + 1.5 IQR was called an outlier (Note: IQR=Q3 - Q1 is the distance between the first and third quartile of the data). a. If you have a standard normal random variable (i.e., N(0,1) ), what value will Q1 and Q3 be equal to? Note that for a random variable, quartiles will correspond to the values that have 25% probability above or below them, rather than that percentage of actual data. b. Calculate the probability that a N(0,1) random variable falls outside the interval (Q1 - 1.5 IQR, Q3+1.5 IQR). c. Suppose you have 100 N(0,1) random variables, each independent of the others. Calculate the probability that none of them will fall outside the interval (Q1- 1.5 IQR, Q3+1.5 IQR). What will happen to this probability if you had 200 instead of 100 normal random variables?

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