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 8.8 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 5 and 10 minutes (b) the response time is less than 5 minutes (c) the response time is more than 10 minutes

Answer #1

Solution :

Given that ,

mean = = 8.8

standard deviation = = 1.9

(a )P(5 < x < 10) = P((5 - 8.8)/ 1.9) < (x - ) / < (10 - 8.8) / 1.9) )

= P(-2 < z < 0.6316)

= P(z < 0.6316) - P(z < -2)

= 0.7362 - 0.0228

= 0.7134

Probability = 0.7134

(b )P(x < 5) = P((x - ) / < (5 - 8.8) / 1.9)

= P(z < -2)

= 0.0228

Probability = 0.0228

(c )P(x > 10) = 1 - P(x < 10)

= 1 - P((x - ) / < (10 - 8.8) / 1.9)

= 1 - P(z < 0.6316)

= 1 - 0.7362

= 0.2638

Probability = 0.2638

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