Maths/statistics

Question

1. Police response time to an emergency call is the difference between the time the call is first received by the dispatcher and the time a patrol car radios that it has arrived at the scene. Over a long period of time, it has been determined that the police response time has a normal distribution with a mean of 8.4 minutes and a standard deviation of 1.4 minutes. For a randomly received emergency call, find the following probabilities.
2. A) the response time is between 10.9 and 11.4 minutes.
3. Incorrect Keep your answer in 4 decimal places.
4. B) the response time is 10.9 to 11 minutes.
5. Incorrect Keep your answer in 4 decimal places.
6. C) the response time is anywhere from 4.2 to less than 10 minutes.
7. Incorrect Keep your answer in 4 decimal places.
8. D) the response time is anywhere greater than 7.7 to 13.6 minutes.
9. Incorrect Keep your answer in 4 decimal places

Answer 1

For each of these, we can subtract the cumulative distribution values at the requested response times.

to calculate the cumulative distribution value, we first need to calculate a z-score by using z=(x-mean)/sd

for example, for 10.9, z =(10.9-8.4)/1.4 = 1.7857

the value of the cumulative standard normal distribution at 1.7857 is 0.9629. That means that 96.29% of response times are less than or equal to 10.9.

so, do the same thing for response time of 11.4

z = (11.4-8.4)/1.4 = 2.143

the value of cumulative standard normal distribution at 2.143 is 0.9839

so probability that response time is between 10.9 and 11.4 is 0.9839 - 0.9629 = 0.02101