Answer to Question #263227 in Statistics and Probability for Vee

Question

The Kepong Automobile Association reports that the average time it takes to respond to an emergency call is 32 minutes. Assume the variable is approximately normally distributed and the standard deviation is 6 minutes. If 100 calls are randomly selected, approximately how many will be responded to in less than 22 minutes?

Answer 1

$Z=\frac{x-\mu}{\sigma}$

$Z=\frac{22-32}{6}=-1.67$

From normal distribution table, it is found that probability is:

$P(X<22) = P(Z<-1.67)= 0.0475$

This means 4.75% of calls will have a response time of less than 22 minutes. If 100 calls are randomly selected;

4.75% of 100 = 4.75 or 5

This means approximately five calls in 100 randomly selected will have response time less than 22 minutes.