Question

the time for a major exam to be completed is normally distributed with an average of 55 minutes and a standard deviation of 9 minutes. If 92% of the student completed the exam, when should the test be terminated?

Answer 1

Given,

Average time $x=55 min$

Standard deviation $\sigma=9min$

Probability os student who completed the exam $=0.92$

As the exam time is normally distributed then The probabilty Who do not complete their exam

$= 1-P(x<0.92)=1-0.92=0.08$

The value of z at 0.08 from the standard table is -1.4

Using normal distribution formula,

$z=\dfrac{x-a}{\sigma}$

$\Rightarrow -1.4\times 9=55-a\\\Rightarrow a=55+12.6=67.6\text{ min}$.

The test Should be terminated at 67.6 min.