Question

2. In each case, determine the value of the constant c that makes each probability statement correct.

(a) P(Z ≥ c) = .05 (3 points)

(b) P(Z < c) = .005 (3 points)

(c) P(−c≤Z≤c)=.5(3points)

Answer 1

Solution :

(a)

P(Z c) = 0.05

1 - P(Z c) = 0.05

P(Z c) = 1 - 0.05 = 0.95

P(Z 1.645) = 0.95

c = 1.645

(b)

P(Z < -2.576) = 0.005

c = -2.576

(c)

P(-c Z c) = 0.5

P(Z c) - P(Z -c) = 0.5

2P(Z c) - 1 = 0.5

2P(Z c) = 1 + 0.5 = 1.5

P(Z c) = 1.5 / 2 = 0.75

P(Z 0.674) = 0.75

P(-0.674 Z 0.674) = 0.5