Answer to Question #166840 in Statistics and Probability for Ivy Grace

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

Mean($\mu$ ) = 55

Standard deviation($\sigma$ )= 9

According to question, P(z) = 0.92

Using Standard Normal Distribution Chart

z= 1.405

By normal distribution formula, $z=\dfrac{\bar x-\mu}{\sigma}$

$1.405=\dfrac{\bar x-55}{9}$

$\Rightarrow \bar x = 67.645$

Hence the test will be terminated after 67.6 minutes.