Question

Exhibit: Standard Normal Distribution.

Calculate the following for the standard normal distribution using Excel. Round your solutions to 4 digits.

Hint: 1) it’s easier to understand the question if you draw a picture for yourself; 2) recall that the standard normal distribution has the mean of 0 and the standard deviation of 1.

A. Refer to the Exhibit Standard Normal Distribution.

Find the value of z such that the area to the right of z is 0.0305.

B. Refer to the Exhibit Standard Normal Distribution.

What is the value of z₀ if P(z ≤ z₀) = 0.1507?

C. Refer to the Exhibit Standard Normal Distribution.

What is the value of z if the area between -z and z is 0.74?

Answer 1

A) The value of Z such that the area to the right of Z is 0.0305 is calculated using excel formula for normal distribution which is =NORM.S.INV(1-0.0305) this results in Z = 1.87.

B) The value of Z₀ if P(Z ≤ Z₀) = 0.1507, the value of Z₀ is calculated using excel formula for normal distribution =NORM.S.INV(0.1507) which results in Z₀ =-1.03

C) The value of Z if the area between -Z and Z is 0.74 is calculated again by excel formula for normal distribution, but as we know that the normal distribution is symmetric hence the area between the mean value and -Z is equal to 0 to Z which will be 0.74/2 = 0.37. Hence the area below -Z will be 0.50-0.37= 0.13.

Now the -Z score is calculated using excel formula =NORM.S.INV(0.13) which results in -Z =-1.13 and hence Z = 1.13