Question

1)What is z0 if

P(z > z₀) = 0.12

P(z < z₀) = 0.2

P(z > z₀) = 0.25

P(z < z₀) = 0.3

Answer 1

Since probabilities are given, we need to perform a reverse lookup of z tables, i.e check the value first and then find the rows and columns to get the z value.

P(z > z0) = 0.12

The value 0.12 is not found in the table. However, the values 0.1190 and 0.1210 have a row number -1.1 and column numbers 0.07 and 0.08 respectively. Therefore, the value of z is (-1.17 + -1.18) / 2 = -1.1750.

P(z < z0) = 0.2

The value nearest to 0.2 is 0.2005 which has row -0.8 and column 0.04. The answer is -0.84.

(Using a calculator however, the exact value comes out to be -0.816.)

P(z > z0) = 0.25

The nearest values have row number -0.6 and column numbers 0.07 and 0.08. The answer is -0.675.

(Using a calculator, the exact value is -0.6745.)

P(z < z0) = 0.3

The nearest values have row number -0.5 and column numbers 0.02 and 0.03. The answer is -0.525.

(Using a calculator, the exact value is -0.5244.)