please Work this problem by hand

Question

.For the following set of scores, fill in the cells. The mean is 70 and the standarddeviation is 8.

 

Raw score	Zscore
68.0	-0.25
57.2	–1.6
82.0	1.5
84.4	1.8
69.0	--0.125
66.0	–0.5
85.0	1.875
83.6	1.7
72.0	.25

Answer 1

Z=(X-m)/S where m=mean=70 S=standard deviation=8. X is the raw score.

Also, X=SZ+m by making X the subject.

By substituting the given value (X or Z) the associated value (Z or X) can be calculated using the appropriate formula, and the table can be completed.

The next step would be to use the normal distribution table to find the probabilities associated with the Z values.

When Z is negative the probability, p, can be found using the formula p=1-N(|Z|) where N is the probability associated with |Z|, the magnitude of Z.

For example, when X=68, Z=(68-70)/8=-2/8=-1/4=-0.25; when Z=-1.6, X=8(-1.6)+70=-12.8+70=57.2.