Now the following problems are quantile problems which ask for values of x on th
ID: 2933402 • Letter: N
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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