Question

Given that z is a standard normal random variable, compute the following probabilities. (Round your answers to four decimal places.)

(a)

P(z ≤ −3.0)

(b)

P(z ≥ −3)

(c)

P(z ≥ −1.3)

(d)

P(−2.4 ≤ z)

(e)

P(−1 < z ≤ 0)

Answer 1

Solution :

(a)

=> P(z <= −3.0) = 1 - P(z > -3.0)

= 1 - P(Z < 3)

= 1 - 0.9987

= 0.0013
(b)

=> P(z >= −3) = 1 - P(Z < -3)

= 1 - [1 − P(Z < 3)]

= P(Z < 3)

= 0.9987

(c)

=> P(z >= −1.3) = 1 - P(Z < -1.3)

= 1 - [1 − P(Z < 1.3)]

= P(Z < 1.3)

= 0.9032

(d)

=> P(−2.4 <= z) = P(Z >= -2.4)

= 1 - P(Z < -2.4)

= 1 - [1 − P(Z < 2.4)]

= P(Z < 2.4)

= 0.9918

(e)

=> P(−1 < z <= 0) = P(Z < 0) - P(Z < -1)

= 0.5 - [1 - P(Z < 1)]

= 0.5 - [1 - 0.8413]

= 0.3413