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3. The following problems are quantile problems that ask for values of x on the x-axis...

3. The following problems are quantile problems that ask for values of x on the x-axis for which certain probabilities (percentile) are true. Please draw the bell curves and shade in regions. Suppose that Z ~ N(0,1) and X ~ N(10,1).

(a) Find the value of a so that P(Z < a) = 0.25

(b) Find the 90th percentile of Z.

(c) Find the value of c such that P(Z > c) = 0.1.

(d) Find the value of d so that P(X < d) = 0.9 based on the value in (b)

(e) If U ~ N(10, 5), find its 90th quantile using (b) or (d)

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