Question

1. The average ACT score for a class of 33 is 21.65, with s=2.83

Covert each of the following to z score:

1. X=19

2. X=25 and

3. X=33

2. The average ACT score for a class of 33 Is 21.65 with s=2.83

What ACT score is 1.5 standard deviations units below the mean?

What score is 2 standard deviation units above the mean?

Answer 1

Solution :

Given that ,

1] mean = = 21.65

standard deviation = = 2.83

1) x = 19

Using z-score formula,

z = x - /   

z = 19 - 21.65 / 2.83

z = -0.94

2) x = 25

Using z-score formula,

z = x - /   

z = 25 - 21.65 / 2.83

z = 1.18

3) x = 33

Using z-score formula,

z = x - /   

z = 33 - 21.65 / 2.83

z = 4.01

2]  mean = = 21.65

standard deviation = = 2.83

1) z = -1.5

Using z-score formula,

x = z * +

x = -1.5 * 2.83 + 21.65

x = 17.41

2) z = 2.00

Using z-score formula,

x = z * +

x = 2.00 * 2.83 + 21.65

x = 27.31