Question

question 11 of 11
a fire department in a rural county reports that its response time to fires is approximately normally distributed with a mean of
22 minutes and a standard deviation of 6.9 minutes. assume that this claim is true.
1% of response times take at least how many minutes? minutes (round to 2 decimal places.)

Explanation:

Step1: Find the z - score

We want to find the value \(x\) such that \(P(X\geq x)=0.01\). Then \(P(X < x)=1 - 0.01=0.99\). Looking up the \(z\) - score in the standard normal distribution table (or using a calculator with a normal - distribution function), the \(z\) - score corresponding to a cumulative probability of \(0.99\) is approximately \(z = 2.33\).

Step2: Use the z - score formula

The z - score formula is \(z=\frac{x-\mu}{\sigma}\), where \(\mu = 22\) (mean), \(\sigma=6.9\) (standard deviation), and \(z = 2.33\).
We solve for \(x\):

$$
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Answer:

\(38.08\)