In: Statistics and Probability
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 6.8 minutes and a standard deviation of 1.9 minutes. For a randomly received emergency call, find the following probabilities. (Round your answers to four decimal places.)
(a) the response time is between 3 and 8 minutes
(b) the response time is less than 3 minutes
(c) the response time is more than 8 minutes
Solution :
Given that ,
(a)
P(3 < x < 8) = P[(3 - 6.8)/ 1.9) < (x - ) / < (8 - 6.8) / 1.9) ]
= P(-2 < z < 0.63)
= P(z < 0.63) - P(z < -2)
= 0.7357 - 0.0228
= 0.7129
Probability = 0.7129
(b)
P(x < 3) = P[(x - ) / < (3 - 6.8) / 1.9]
= P(z < -2)
= 0.0228
Probability = 0.0228
(c)
P(x > 8) = 1 - P(x < 8)
= 1 - P[(x - ) / < (8 - 6.8) / 1.9)
= 1 - P(z < 0.63)
= 1 - 0.7357
= 0.2643
Probability = 0.2643