Response Time

Question

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 8.1 minutes and a standard deviation of 1.4 minutes. For a randomly received emergency call, find the following probabilities. (Round your answers to four decimal places.)

 

(a) the response time is between 5 and 10 minutes



(b) the response time is less than 5 minutes



(c) the response time is more than 10 minute

Answer 1

(a) With a mean of 8.1 and s.d. of 1.4 you need to convert 5 and 10 to z-values:

 

z=(x-μ)/σ

 

z₁ = (5-8.1)/1.4   and  z₂ = (10-8.1)/1.4

 

Use these two values of z to find the appropriate probabilities in a normal distribution table; see:

 

https://www.wyzant.com/resources/files/392716/normal_dist_table

 

Because the x values are on either side of the mean add the values you get from the table.

 

 

(b) and (c) also calculate the z-values, draw the curve, and choose the appropriate area.

 

 

 

If you need more explanation please comment back.

 

 

Kemba, I see you have several statistics and probability questions here. I teach classes in statistics and probability as well as other math courses. I would be able to help you answer these types of questions on your own. Click on my profile picture and send me a direct message if you are interested.

Arnold