Question

In each case, determine the value of the constant c that makes the probability statement correct. (Round your answers to two decimal places.)

(a)    Φ(c) = 0.9854


(b)    P(0 ≤ Z ≤ c) = 0.3078


(c)    P(c ≤ Z) = 0.1210


(d)    P(−c ≤ Z ≤ c) = 0.6680


(e)    P(c ≤ |Z|) = 0.0160

You may need to use the appropriate table in the Appendix of Tables to answer this question.

Answer 1

Solution :

Using standard normal table,

Solution :

Using standard normal table,

(a)

= 0.9854

P(Z < z) = 0.9854

P(Z < 2.18) = 0.9854

c = 2.18

(b)

P( 0 z c) = 0.3078

P(Z c) - P(Z 0) = 0.3078

P(Z c) = P(Z 0) + 0.3078

P(Z c) = 0.5 + 0.3078 = 0.8078

P(Z 0.87) = 0.8078

c = 0.87

(c)

P(c Z) = 0.1210

P(Z c) = 0.1210

1 - P(Z c) = 0.120

P(Z c) = 1 - 0.1210 = 0.879

P(Z 1.17) = 0.879

c = 1.17

(d)

P(-c Z c) = 0.6680

P(Z c) - P(Z -c) = 0.6680

2P(Z c) - 1 = 0.6680

2P(Z c) = 1 + 0.6680 = 1.6680

P(Z c) = 1.6680 / 2 = 0.8340

P(Z 0.97) = 0.8340

c = 0.97

(e)

P(c |Z|) = 0.0160

2 * [1 - P(z < c)] = 0.0160

1 - P(z < c) = 0.0160 / 2 = 0.008

P(z < c) = 1 - 0.008 = 0.992

P(z < 2.41) = 0.992

c = 2.41