Question

2. Determine Z when the probability is known

1. What Z corresponds to the 10^th percentile?
2. What Z score corresponds to the 80^th percentile?
3. What Z score corresponds to the 90^th percentile?
4. What Z score corresponds to the 50^th percentile?
5. What Z score corresponds to the 60^th percentile?
6. P (0 < Z < ?) = .1700
7. P (0 < Z < ?) = .3997
8. P ( Z > ? ) = .1587
1. P (Z > ?) = .0968
10. P (? < Z < 0) = .3413

Answer 1

a) P(Z<z) =0.1

From standard normal table, we have z = -2.327.

b) P(Z<z) =0.8

From standard normal table, we have z = 0.84

c) P(Z<z) = 0.9

From standard normal table, we have z = 1.28

d) P(Z<z) = 0.5

From standard normal table, we have z = 0

e) P(Z<z) = 0.6

From standard normal table, we have z = 0.25

f) P(0<Z<?) = 0.17

P(Z<?) - 0.5 = 0.17

P(Z<?) = 0.67

From standard normal table, we have ? =0.44

g) P(0<Z<?) = 0.3997

P(Z<?) - 0.5 = 0.3997

P(Z<?) = 0.8997

From standard normal table, we have ? = 1.28

h) P(Z>?) = 0.1587

1- P(Z<?) = 0.1587

P(Z<?) = 0.8413

From standard normal table, we have ? = 1

i) P(Z>?) = 0.0968

1- P(Z<?) = 0.0968

P(Z<?) = 0.9032

From standard normal table, we have ? = 1.3

j) P(?<Z<0) = 0.3413

P(0<Z>?) = 0.3413

P(Z<?) - 0.5 = 0.3413

P(z<?) = 0.8413

From standard normal table, we have ? = 1