Question

Find the value of z such that 0.5762

0.5762
of the area lies between −z
−
z
and z. Round your answer to two decimal places.

Answer 1

z = 0.80

Explanation:

You want the value of z such that p(-z < X < z) = 0.5762 for a normal distribution.

Tails

The area outside the region of interest will be split evenly between the two tails. That is, the lower tail will hold (1 -0.5762)/2 = 0.2119 of the area of the distribution. The required value of z will be the magnitude of the Inverse CDF function for this value.

Inverse CDF

The attached calculator shows the required value of z is about 0.80.