Question

3. (6 pts) Fire department response time is the length of time it takes a fire truck to arrive at

the scene of a fire starting from the time the call was given to the truck. Response time
for the Castle Wood Fire Department follows a mound shaped and symmetrical
distribution. The response time has mean = 8.8 minutes with standard deviation o=
2.1 minutes. If a random sample of 32 response times is taken and the mean response
time is computed, find each of the following.
a. P(x ≥9)
b. P(8≤x≤9)

Answer 1

a. P(mean ≥ 9) ≈ 0.2950

b. P(8 ≤ mean ≤ 9) ≈ 0.6894

Explanation:

For a sample size of 32 taken from a population with a mean of 8.8 and a standard deviation of 2.1, you want to know ...

• probability the sample mean is 9 or more
• probability the sample mean is between 8 and 9.

Sample distribution

The mean of the distribution of sample means is the same as the population mean, 8.8.

The standard deviation of the sample means is the population standard deviation divided by the root of the number of samples: 2.1/√32.

Probabilities

A suitable calculator can find the necessary probabilities, given the parameters of the distribution of sample means. The attachment shows the calculation.

a. P(mean ≥ 9) ≈ 0.2950

b. P(8 ≤ mean ≤ 9) ≈ 0.6894