Answer to Question #263199 in Statistics and Probability for sha

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

$μ=32\\ σ=6\\ P(X<22)=P(Z<(22−32)/6) ​=P(Z<−1.67)\\ =0.04746\\ =4.746$

$N=0.04746×100=5\ \text{call}\\$