Question

For a random variable Z, that follows a standard normal distribution, find the values of z required for these probability values

1. P(Z<z)=.5
2. P(Z<z)=.1587
3. P(Z<z)=.8413

Answer 1

We have given the probabilities of Standard Normal distribution, and we have asked the corresponding z values ( i.e Z score ).

a) Here we have given probability = 0.5

By using Standard Normal table we get-

z= -0.00 (Rounded to two decimal places)

We can also find the Z score value in excel.

In excel use the command =NORMSINV(probability)

It will give you the corresponding Z score.

b) Here we have probability= 0.1587

Therefore we get z = NORMSINV(0.1587) = -1.00   (Rounded to two decimal places)

c) We have probability = 0.8413

Therefore we get z = NORMSINV(0.8413) = 1.00   (Rounded to two decimal places)

Hope this will help you. Thank you :)