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 house 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 between 4 and 6 minutes?

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shivishivangi1679 shivishivangi1679 · Answer 1 · 2022-06-17T15:28:34+02:00

Using the normal distribution, it is found that the 10.56% of fire station response times are under 3 minutes.

If we've got a normal distribution, then we can convert it to a standard normal distribution and its values will give us the z score.

If we have

[tex]X \sim N(\mu, \sigma)[/tex]

(X is following a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex])

then it can be converted to a standard normal distribution as

[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z \sim N(0,1)[/tex]

The mean is of 4.5 minutes,

The standard deviation is of 1.2 minutes,

The proportion of fire station response times are under 3 minutes is the p-value of Z when X = 3, hence:

[tex]Z = \dfrac{X - \mu}{\sigma}, \\\\Z = \dfrac{3 - 4.5}{1.2}, \\\\Z = -1.25[/tex]

-1.25 has a p-value of 0.1056.

0.1056 x 100% = 10.56%

10.56% of fire station response times are under 3 minutes.

To learn more about the normal distribution, brainly.com/question/24663213

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