Can you please work out the following question For a distrib

Can you please work out the following question: For a distribution of scores, X= 40 corresponds to a z score of z= +1.00, and X=28 corresponds to a z-score of z= -0.50. What are the values for the mean and standard deviation for the distribution. Hint: Sketch a distribution and locate each of the z-score position.

Solution

working out the formula of z-score, we can write:

(40-mu)/sigma = 1 => 40-mu = sigma

(28-mu)/sigma = -0.5 => 28 - mu = -0.5 sigma

On solving, we get: mu = 32, sigma = 8