Now the following problems are quantile problems which ask for values of x on th

Question

Now the following problems are quantile problems which ask for values of x on the x-axis for which certain probabilities are true. Make sure you draw bell curves and shade in regions just like the procedure I showed you in class to solve the following problems. Suppose that Z ~ N(0; 1) and X ~ N( = 2; = 3).

(e) Find the value c such that P(Z > c) - 0.1.
(f) Find the value of b such that P(|Z| < b) = 0.95
(g) Find the value of b such that P(|Z| < b) = 0.95
(h) Find the value c such that P((X < 2) U (X > c)) = 0.95

Thank you!

Explanation / Answer

Answer to the questions:

X ~ N( Mu = 2, Sigma = 3)

e. P(X>c) = .1

Z = 1.28, so c-2 / 3 = 1.28

So, c = 3*1.28+2 = 5.84

f. P(|Z|<b) = .95

So, P(-Z<b<Z) = .95

(b-2)/3 = 1.645

b = 3*1.645+2 = 6.935

g. P(|Z|<b) = .95

Again it is same as f, hence, b = 6.935

g. P( X<2 U (X>c)) = .95

P(X<2) = P(Z< 2-2/3) = .5

So, P(X>c) = .95-.5 = .45

Z = .125 for P(X>c) = .45

(c-2)/3 = .125

c = .125*3+2 = 2.375

c = 2.375

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