Question

1. If the mean of a distribution is 100 with a standard deviation of 10, what z-score is associated with a raw score of X=90?

2. If the mean of a distribution is 100 with a standard deviation of 10, what raw score is associated with a z-score of +2.003.

3. Using the z-score formula, if you have a distribution with a mean of 50 and a standard deviation of 5, what z-score is associated with a raw score of X=43.5?

4. Using the z-score formula, if you have a distribution with a mean of 50 and a standard deviation of 5, what z-score is associated with a raw score of X=53.1

Answer 1

1)

Solution :

Given that ,

mean = = 100

standard deviation = = 10

x = 90

z = (x - ) / = (90 - 100) / 10 = -10 / 10 = -1

z-score = -1