Question

1) What is the variance of scores of 0, 1, 1, 2?

2) If a raw score is 28, M = 20, and SD = 2. The Z score is ?

3) What Z score would a person need to be in the top 5% of his or her class on a particular test? (Assume a normal distribution.)

please help

Answer 1

Solution:

1) Given that,

0, 1, 1, 2

n = 4

The mean of sample is   

x/n =  (0 + 1 + 1 + 2  / 4)

   = 4 / 4

= 1

The sample mean is = 1

The populatio variance is  2 =

2  = n /(x - )2

2  = 4 (0 - 1)2+ (1 - 1)2+ (1 - 1)2+ ( 2 - 1 )2

2 = 4 (1 + 0 + 0 + 1)

2 = 2 / 4

2 = 0.5

2) Given that ,

mean = = 20

standard deviation =  = 2

x = 28

Using z-score formula,

z = x - /   

z = 28 - 20 / 2

z = 4

3) Using standard normal table,

P(Z > z) = 5%

= 1 - P(Z < z) = 0.05

= P(Z < z) = 1 - 0.05

= P(Z < z ) = 0.95

= P(Z < 1.645 ) = 0.95

z = 1.645