An auto assoc reports that the average time it takes to respond to an emergency call is 25 minutes. Assume the variable is approx normally distributed and the standard deviation is 4.5 minutes. If 95 calls are randomly selected, approx how many will be responded to in less than 24 minutes?

The way to approiach this problem is to determine the "z-score" of the data point 24 minutes, which means how many standard deviations it is away fom the mean. Then look up the cumulative probability value for that Z-score, and that will tell you what percentage of the calls are responsed to in less than 24 minutes. The cumulative probability is the area under the normal curver from negative infinity to the z-score in question.

The z-score is calculated as the difference between the point in question and the mean divided by the standard deviation:



Your text book should have a list of cumulative probabilities versus z-scores for normal distributions. Post back with your answer and we'll check it for you.