contestada

For a sample of n = 100 scores, x = 45 corresponds to z = 0.50 and x = 52 corresponds to z = +1.00. what are the values for the sample mean and standard deviation? m = 31 and s = 7 m = 31 and s = 14 m = 38 and s = 7 m = 38 and s = 14

Respuesta :

barnuts

We are given a fixed number of samples, n = 100.

We are given two conditions:

x = 45, z = 0.50

x = 52, z = 1.00

 

The relevant equation we can use here is:

z = (x – m) / s

where m is the mean and s is the std dev

 

So for the two conditions:

0.50 = (45 – m) / s                            --> eqtn 1

1.00 = (52 – m) / s                            --> eqtn 2

 

Rewriting eqtn 1 in terms of m:

0.5 s = 45 – m

m = 45 – 0.5 s                                     --> eqtn 3

 

Rewriting eqtn 2 in terms of m:

1.00 s = 52 – m

m = 52 – 1.00 s                                   --> eqtn 4

 

Equating eqtn 3 and 4:

45 – 0.5 s = 52 – 1.00 s

0.5 s = 7

s = 14

 

From eqtn 4:

m = 52 - 1.00 * 14

m = 38

 

 

Therefore answers are:

 m = 38 and s = 14

Otras preguntas