Question

1.

a) For a standard normal distribution, find c if P(z < c) = 0.4756 c =

b) For a standard normal distribution, find c if P(z > c) = 0.2399 For greatest accuracy, don't use Z tables. c =

Answer 1

The z score is a standardized test statistic which tells us how many standard deviation away from the mean (above if it is positive, below if it is negative). It is called standardized as it is comparable to a normal (bell curved) distribution having mean (\mu) = 0 and standard deviation (\sigma) = 1.

Please note:

(i) If the p value is greater than 0.5, the Z value is positive (it lies to the right of the mean)

(ii) If the p value is less than 0.5, the Z value is negative (it lies to the left of the mean)

(iii) If we are given the p value to the right of Z, we convert it to a p value to the left, and then find the z values as the normal tables gives us p values to the left only.

_______________________________________________

(a) P(Z < c) = 0.4756

Using Excel Function NORMSINV(0.4756), c = -0.061

_____________________________________________

(a) P(Z > c) = 0.2399

Since z probabilities lie to the left, P(Z < c) = 1 - P(Z > c) = 1 - 0.2399 = 0.7601

Using Excel Function NORMSINV(0.7601), c = 0.707

_____________________________________________