## Question 70:

Asked on December 10, 2007

Tags:
Z-Score ,
Percentile

1

## Answer:

No answer provided yet.We need to use z-scores here to figure out the percentile grade cut-offs. We know the mean and standard deviation so we just need to figure out what data point we would use to get the z-scores that correspond to A:90, B:80, C:70, D:60, F:50 percent.

- The easiest way I can think of doing this is setting up a simple equation and solve for the unknown scores from the z-scores for each percentile.
- Find the z-scores for the percentiles 90, 80, 70 , 60 (we know 50 is 0). To do this you can use the percentile to z-score calculator.. We’re interested only on one-side of the area of the curve since a negative score is neither possible nor desirable (choose 1-sided) and get the z-scores for all cut-offs. For example you should get 1.28 for 90% (enter .90).
- Setup the equation for each z-score. For example, for 90% the equation should be
( X – 75 ) / 9 = 1.28. Then isolate and solve for X (X-75 = 11.53396 so X = 86.53). Repeat this process for all scores.
You should get the following:

Percentile | Z | Score | Grade |
---|

>=90 | >=1.28 | >=86.53 | A |

80 | .841 | 82.57 | B |

70 | .524 | 79.72 | C |

60 | .253 | 77.28 | D |

<60 | <.253 | <77.28 | F |