Question

Find the following z values for the standard normal variable Z. (You may find it useful to reference the z table. Negative values should be indicated by a minus sign. Round your answers to 3 decimal places.) a. P(Z ≤ z) = 0.1020 b. P(z ≤ Z ≤ 0) = 0.1772 c. P(Z > z) = 0.9929 d. P(0.40 ≤ Z ≤ z)= 0.3368

Answer 1

1. P(Z ≤ z) = 0.1020

The z critical value table given the value in the form of P(Z ≤ z)

The area under z value is 0.1020.

The z value of corresponding area is 0.1020

P(Z ≤ -1.27) = 0.1020

b. P(z ≤ Z ≤ 0) = 0.1772

(Z≤ 0) – P(Z ≤ z) = 0.1772

The area below 0 is 0.50 because standard normal distribution has mean 0.

P(Z ≤ z) = 0.5 – 0.1772 = 0.3228

The z value of corresponding area is 0.3228

P(Z ≤ -0.46) = 0.3228

P(-0.46 ≤ Z ≤ 0) = 0.1772

c. P(Z > z) = 0.9929

P(Z ≤ z) = 1 – 0.9929

P(Z ≤ z ) = 0.0071

The z value of corresponding area is 0.0071

P(Z ≤ -2.45) = 0.0071

P(Z > -2.45) = 0.9929

d. P(0.40 ≤ Z ≤ z)= 0.3368

(Z≤ z) – P(Z ≤ 0.40) = 0.3368

The area corresponding z value

P(Z ≤ 0.40) = 0.6554

P(Z ≤ z) = 0.3368 + 0.6554 = 0.9922

The z value of corresponding area is 0.5218

P(Z ≤ 2.42) = 0.9922

P(0.40 ≤ Z ≤ 2.42)= 0.3368