Question 716:

Asked on May 5, 2009

Tags: Z-Score

1

Answer:

No answer provided yet.We can use the formula for the z-score for a datapoint to solve this one. The formula is (datapoint-mean)/standard deviation = z-score. Before we do this, we need to find the z-scores for the three proportions .80, .90 and .95 using a table of normal values for 1-sided area (or the excel function =NORMSINV() ).
We get the z-scores of .841621, 1.28155 and 1.64485.

Now we substitute each of these into the z-score equation to solve for the unknown score.

1. (data-point-mean)/standard deviation = z-score
2. (data-point-90)/10= .841621
3. data-point-90= 8.41621
4. data-point= 98.41621

Repeating this process for the other 2 values we get 102.8155 and 106.4485.  So to be 80% sure they need a score of 98.41621, 90% sure 102.8155 and 95% sure a score of 106.4485.