Question

Find the following probabilities based on the standard normal variable Z. (You may find it useful to reference the z table. Round your answers to 4 decimal places.) a.P(Z > 0.62)b.P(Z ≤ −1.71)c.P(0 ≤ Z ≤ 1.83)d.P(−0.66 ≤ Z ≤ 2.65)

Answer 1

Solution :

a. => P(Z > 0.62) = 1 − P(Z < 0.62)

= 1 − 0.7324

= 0.2676

b. => P(Z <= −1.71) = 1 − P(Z <= 1.71)

= 1 − 0.9564

= 0.0436

c. => P(0 <= Z <= 1.83) = P(Z <= 1.83) - P(Z <= 0)

= 0.9664 - 0.5

= 0.4664

d. => P(-0.66 <= Z <= 2.65) = P(Z <= 2.65) - P(Z < -0.66)

= 0.9960 - (1 - P(Z <= 0.66))

= 0.9960 - (1 - 0.7454)

= 0.7414