Answer to Question #315011 in Statistics and Probability for Iyang

Question

The average time it takes a group of college students to a certain examination is 57.3 minutes . The standard deviation is 9 minutes . Assume that the variable is normally distributed. What is the Probability that a randomly selected college student will complete the examination in less than 54 minutes

Answer 1

$P\left( X\leqslant 54 \right) =P\left( \frac{X-57.3}{\sigma}\leqslant \frac{54-57.3}{9} \right) =P\left( Z\leqslant -0.3667 \right) =\varPhi \left( -0.3667 \right) =0.3569$