Question

Calculate the following probabilities using the standard normal distribution. (Round your answers to four decimal places.)

(a)    

P(0.0 ≤ Z ≤ 1.6)

(b)    

P(−0.1 ≤ Z ≤ 0.0)

(c)    

P(0.0 ≤ Z ≤ 1.49)

(d)    

P(0.6 ≤ Z ≤ 1.51)

(e)    

P(−2.05 ≤ Z ≤ −1.76)

(f)    

P(−0.02 ≤ Z ≤ 3.54)

(g)    

P(Z ≥ 2.60)

(h)    

P(Z ≤ 1.66)

(i)    

P(Z ≥ 6)

(j)    

P(Z ≥ −8)

Answer 1

Solution :

(a)

P(0.0 ≤ Z ≤ 1.6) = P(z < 1.6) - P(z < 0) = 0.4452

(b)

P(−0.1 ≤ Z ≤ 0.0) = P(z < 0) - P(z < -1) = 0.3413

(c)

P(0.0 ≤ Z ≤ 1.49) = P(z < 1.49) - P(z < 0) = 0.4319

(d)

P(0.6 ≤ Z ≤ 1.51) = P(z < 1.51) - P(z < 0.60 = 0.2087

(e)

P(−2.05 ≤ Z ≤ −1.76) = P(z < -1.76) - P(z < -2.05) = 0.0190

(f)

P(−0.02 ≤ Z ≤ 3.54) = P(z < 3.54) - P(z < -0.02) = 0.5078

(g)

P(z > 2.60) = 1 -P(z < 2.60) = 0.0047

(h)

P(z < 1.66) = 0.9515

(i)

P(z > 6) = 1 - P(z < 6) = 1 - 1 = 0

(j)

P(z > -8) = 1 - P(z < -8) = 1 - 0 = 1