Question

Find these probabilities for a standard normal random variable Z. Be sure to draw a picture to check your calculations. Use the normal table or software.

​(a) ​P(Zless than<1.11.1​)	​(d) ​P(StartAbsoluteValue Upper Z EndAbsoluteValueZgreater than>0.40.4​)
​(b) ​P(Zgreater than>negative 1.4−1.4​)	​(e) ​P(negative 1.4−1.4less than or equals≤Zless than or equals≤1.11.1​)
​(c) ​P(StartAbsoluteValue Upper Z EndAbsoluteValueZless than<1.61.6​)

Answer 1

a) P(Z < 1.1) = 0.8643

b) P(Z > -1.4) = 1 - P(Z < -1.4) = 1 - 0.0808 = 0.9192

c) P(|Z| < 1.6) = P(-1.6 < Z < 1.6) = P(Z < 1.6) - P(Z < -1.6) = 0.9452 - 0.0548 = 0.8904

d) P(|Z| > 0.4) = 1 - P(|Z| < 0.4) = 1 - P(-0.4 < Z < 0.4) = 1 - (P(Z < 0.4) - P(Z < -0.4)) = 1 - (0.6554 - 0.3446) = 0.6892

e) P(-1.4 < Z < 1.1) = P(Z < 1.1) - P(Z < -1.4) = 0.8643 - 0.0808 = 0.7835