Question

Consider the standard normal curve, where μ=0 and σ=1.

Find the value z so that 90% of the area under the curve is between −z and z . Give your answer to 4 decimal places.

Answer 1

Solution:

We have to find the value of z so that 90% area under the curve is between -z to z.

That is find

P(-z<Z<z)=90%

That is find

P(-z<Z<z)=0.90

Area between -z to z is 0.90, then area in two tails is

=1-0.90=0.10

Thus area in left tail =0.10/2=0.05

Thus find z value for left tail area=0.05

Use following steps in TI 84 plus calculator

Press 2ND and Press VARS

Select invNorm

Enter numbers

Thus z value=-1.6449

Thus absolute z value=1.6449

Thus required answer is 1.6449