Question

Find the following probabilities for the standard normal random variable z z :

a) P(−2.07≤z≤1.93)= P ( − 2.07 ≤ z ≤ 1.93 ) =

(b) P(−0.46≤z≤1.73)= P ( − 0.46 ≤ z ≤ 1.73 ) =

(c) P(z≤1.44)= P ( z ≤ 1.44 ) =

(d) P(z>−1.57)= P ( z > − 1.57 ) =

Answer 1

Solution:

Given that,

Using standard normal table;

(a)

P(-2.07 z 1.93)

= P(z 1.93) - P(z -2.07)

= 0.9732 - 0.0192

= 0.954

P(-2.07 z 1.93) = 0.954

(b)

P(-0.46 z 1.73)

= P(z 1.73) - P(z -0.46)

= 0.9582 - 0.3228

= 0.6354

P(-0.46 z 1.73) = 0.6354

(c)

P(z 1.44) = 1 - P(z 1.44) = 1 - 0.9251 = 0.0749

(d)

P(z > -1.57) = 1 - P(z < -1.57) = 1 - 0.0582 = 0.9418