Answer Happy

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 2.2 minutes. For a randomly received emergency call, find the following probabilities. (a) the response time is between 4 and 10 minutes (b) the response time is less than 4 minutes (c) the response time is more than 10 minutes
(a) the response time is between 4 and 10 minutes We are asked to find the probability that the police response time will be within a certain interval of time. First, to find probabilities and areas for a random variable: that follows a normal distribution with mean = 8.4 and standard deviation = 2.2, we must convert the given measurements x :- H to z values. Recall that the formula z = z = We want to find the probability that a response time will be between For x = 4 with = 8.4 and = 2.2, we have the following z value. x-μ 0 = 10 = 0.7445 x-μ 0 10 X-8.4 = 0.2427 2.2 For x = 10 with μ = 8.4 and a = 2.2, we have the following z value, rounded to two decimal places. x ✓ 2.2 0 X is used to convert x values to z values. - 8.4 and 10 minutes. So, we need to convert x = 4 and x = 10 to z values.