Question

the average time it takes for a college student to complete a certain examination is 46.2 minutes.the standard deviation is 8 minutes.assume the variable is normally distributed. find the probability that a randomly selected college student will complete the examination in less than 43 minutes

Answer 1

$P(X<x)=P(Z<\frac{x-\mu}{\sigma})$

$P(X<43)=P(Z<\frac{43-46.2}{8})=P(Z<-0.4)$

From table of cumulative standard normal distribution, it is found that the probability of a randomly selected college student will complete the examination in less than 43 minutes is:

$P(X<43) = P(Z<-0.4)=0.3446$