Question

A civil service exam yields scores which are normally distributed with a mean of 81 and a standard deviation of 5.5. If the civil service wishes to set a cut-off score on the exam so that 15% of the test takers fail the exam, what should the cut-off score be? Remember to round your z-value to 2 decimal places.

Answer 1

The cutoff score should be 75.8 marks

Explanation:

The cut-off should be set as the value corresponding to an area 15% in the normal distribution diagram.

Using the standard distribution tables we have value of standard normal deviate (Z) corresponding to area of 15% = -1.04

Thus we have

`-1.04=\frac{X-\bar{X}}{\sigma }\\\\X=-1.04* 5.5+81\\X=75.8`