Response time is an important statistic for measuring the effectiveness of a fire department, and is measured as the difference between the time a fire station receives a call and the time the first piece of fire equipment leaves the station. The response times for fire departments in a large city are found to have an approximately Normal distribution, with a mean of 4.5 minutes and a standard deviation of 1.2 minutes. What percentage of fire station response times are under 3 minutes?Find the z-table here.
Convert 3 minutes to a z-score: z = (3 − 4.5) / 1.2 = −1.25. The standard Normal distribution gives a probability of about 0.1056 to the left of z = −1.25, so about 10.56% of response times are under 3 minutes. The correct choice is 10.56%.
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