response time is an important statistic for measuring the effectiveness of a fire department, and is…

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. 6.68% 10.56% 89.44% 93.32%

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. 6.68% 10.56% 89.44% 93.32%

Answer

Answer:

B. 10.56%

Explanation:

Step1: Calculate the z - score

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$, where $x = 3$ (the value we are interested in), $\mu=4.5$ (the mean), and $\sigma = 1.2$ (the standard deviation). So, $z=\frac{3 - 4.5}{1.2}=\frac{- 1.5}{1.2}=-1.25$.

Step2: Use the z - table

Looking up the z - score of - 1.25 in the standard normal (z) table, the corresponding cumulative probability is 0.1056. This means that the percentage of fire station response times under 3 minutes is 10.56%.