Calculate the following probabilities using the standard normal distribution. Sk

Question

Calculate the following probabilities using the standard normal distribution. Sketch the probability distribution in each case, shading in the area of the calculated probability.

(a) Pr(Z < 0.0)
(b) Pr(Z 1.0)
(c) Pr(Z > 1.96)
(d) Pr(Z < –2.0)
(e) Pr(Z > 1.645)
(f) Pr(Z > –1.645)
(g) Pr(–1.96 < Z < 1.96)
h. Pr(Z < 2.576 or Z > 2.576)
i. Pr(Z > z) = 0.10; find z.
j. Pr(Z < –z or Z > z) = 0.05; find z.

Find the following probabilities:
(a) Y is distributed . Find Pr(Y > 9.49).
(b) Y is distributed t. Find Pr(Y > –0.5).
(c) Y is distributed F4,. Find Pr(Y < 3.32).
(d) Y is distributed N(500, 10000). Find Pr(Y > 696 or Y < 304).

Explanation / Answer

(a) Pr(Z < 0.0) =0.5 (b) Pr(Z = 1.0)= 0.8413 (c) Pr(Z > 1.96)=0.0249 (d) Pr(Z < –2.0)= 0.0227 (e) Pr(Z > 1.645)= 0.0499 (f) Pr(Z > –1.645)= 0.95 (g) Pr(–1.96 2.576) = 1 i. Pr(Z > z) = 0.10; find z = 1.28 j. Pr(Z < –z or Z > z) = 0.05; find z = 1.96

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