Answer to Question #214063 in Statistics and Probability for FJ_Meyers

Question

 The American Automobile Association reports that the average time it takes to respond to an emergency call is 25 minutes. Assume the variable is approximately normally distributed and the standard deviation is 4.5 minutes. If 80 calls are randomly selected, approximately how many will be responded to in less than 15 minutes? 

Answer 1

$\mu=25 \\ \sigma=4.5 \\ P(X<15) = P(Z< \frac{15-25}{4.5}) \\ = P(Z< -2.22) \\ = 0.0132 \\ = 1.032 \; \% \\ N = 0.0132 \times 80 = 1 \;call$