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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
Step 1 (a) the response time is between and 10 minutes We are asked to find the probability that the police response time will be within a certain interval f time. First, to find probabilities and areas for a random variable x that follows normal distribution with mean = 8.4 and standard deviation = 2.2, we must convert the given measurements x to z values. Recall that the formula z = is used to convert x values to z values. We want to find the probability that a response time will be between 4 and 10 minutes. So, we need to convert x = 4 and x = 10 to z values. z = For x = 4 with = 8.4 and = 2.2, we have the following z value. = 7 = x-μ = 2.2 0 For x = 10 with μ = 8.4 and = 2.2, we have the following z value, rounded to two decimal places. x-μ x-μ 8.4 2.2 ( - 8.4
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