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 10.4 minutes and a standard deviation of 1.7 minutes. For a randomly received emergency call, find the following probabilities. (Round your answers to four decimal places.)

(a) the response time is between 7 and 12 minutes


(b) the response time is less than 7 minutes


(c) the response time is more than 12 minutes

B.

Find z such that 95.1% of the standard normal curve lies to the right of z. (Round your answer to two decimal places.)
z =

Answer 1

Answer a) 0.8036

P (−2<Z<0.94 ) = P ( Z<0.94 )−P (Z<−2 ) = 0.8264 - 0.0228

P (−2<Z<0.94 ) = 0.8036

Answer b) 0.0228

Answer c) 0.1736

Answer B. z = -1.65

We have to find value of z such that P(Z > z) = 0.951

P(Z > z) = 1 - P(Z < z)

P(Z < z) = 1 - 1 - P(Z > z) = 1 - 0.951

P(Z < z) = 0.049

From the standard normal table, we can see that value of z corresponding to P(Z < z) = 0.049 is -1.65 (Screenshot of standard normal given below)

z = -1.65