Question

(1 point) Let Z be a standard normal random variable. In each of the following, find the number zo which makes the indicated probability statement correct. (a) P(Z zo)-0.9343 Z0 (b) P(-Zo S Z zo) -0,781 Zo - (c) P(-zo K Z K zo) 0.64 Zo (d) P(Z 2 zo) 0.2914 (e) P(-Zo KZ30)-0.2319 (0 P(-1.51SZS zo) 0.5152 Zo

Answer 1

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We have used the Z tables to solve this problem

a. P(z<=z0) = .9343
z0 = 1.5086

b. P(-z0<=Z<=z0) = .781
P(0<Z<z0) = .781/2 = .3905
P(Z<z0) = .3905+.5 = .8905, z0 = 1.2292

c. P(-z0<=Z<=z0) = .64
P(0<Z<z0) = .64/2 = .32
P(Z<z0) = .82
z0 = 0.9154

d. P(Z>=z0) = .2914
then P(Z<z0) = 1-.2914 = .7086
z0 = 0.5493

e. P(-z0<=Z<0) = .2319
P(Z<=-z0) = .5-.2319 = .2681
z0 = -0.6186

f. P(-1.51<=Z<=z0) = .5152
P(Z<=z0) - P(Z<=-1.51) = .5152
P(Z<=z0)-0.0655 = .5152
P(Z<=z0) = .5152+.0655 = 0.5807
z0 = 0.2037