Statistics Question

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 8.0 minutes and a standard deviation of 1.5 minutes. For a randomly received emergency call, find the following probabilities. (For each answer, enter a number. Round your answers to four decimal places.)

(a)

 the response time is between 5 and 9 minutes

 

(b)

 the response time is less than 5 minutes

 

(c)

 the response time is more than 9 minutes

 

Answer 1

Pictorially, the first problem looks like this:

You are trying to determine the area under the normal curve between 5 and 9 minutes. To do so using a TI-84 calculator, use the "distr" button (press the blue 2nd button then the vars button which is 3 buttons up from the 9). Select "2:normalcdf(". For "lower" enter "5", for "upper" enter "9", for "μ" enter "8" and for "σ" enter "1.5". Highlight "Paste" and hit "enter" then hit "enter" a second time. You should get 0.724757471 which rounds to 0.7248

For question b) use a "lower" value of a very large negative number (say -1000000) and an "upper" of "5".

For question c) use a lower value of "9" and an upper value of a very large number (say 1000000)