Question

1. Find

a. P(Z=-1.01)

b. P(Z>10)

c. P(-1.5<Z<2)

d. P(-2.58<Z)

e. P(Z<3.15)

f. The 30th percentile of Z

g. The z value with 12% area to its right.

2. If X is normally distributed with a mean of 5.6 and a variance of 27, find

a. P(X<2)

b. P(-2.5<X<7.2)

c. The 80th percentile of X

Answer 1

1)

a)

P(Z >= -1) = P(Z < 1)

= 0.8413

b)

P(Z > 10) = 0

c)

P(-1.5 < Z< 2) = P(Z < 2) - P(Z < -1.5)  

= 0.9772 - 0.0668

= 0.9104

d)

P(-2.58 < z) = P(Z > -2.58)

= P(Z < 2.58)

= 0.9951

e)

P(Z < 3.15) =  0.9992

f)

P(Z < z) = 0.30

From Z table, z-score for the probability of 0.30 is -0.5244

30th percentile = -0.52

g)

P(Z > z) = 0.12

= P(Z < z) = 0.88

From Z table, z-score for the probability of 0.88 is 1.175

z = 1.18