Question

1. Police response time to an emergency call is the difference between the time the call is first received and the time a patrol car arrives at the scene. Over along period of time, it has been determined that the police response time is normally distributed with a mean of 8.4 minutes and a standard deviation of 7 minutes. For a randomly received emergency call, what is the probability that the response time will be:
   1. Between 5 and 10 minutes
   2. Less than 5 minutes
   3. More than 10 minutes

Answer 1

Solution :

Given that ,

mean = = 8.4

standard deviation = = 7

a)

P(5 < x < 10) = P((5 - 8.4)/ 7) < (x - ) /  < (10 - 8.4) / 7) )

= P(-0.49 < z < 0.23)

= P(z < 0.23) - P(z < -0.49)

= 0.5910 - 0.3121     Using standard normal table,

= 0.2789

Probability = 0.2789

b)

P(x < 5) = P((x - ) / < (5 - 8.4) / 7)

= P(z < -0.49)

= 0.3121 Using standard normal table,

Probability = 0.3121

c)

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

= 1 - P((x - ) / < (10 - 8.4) / 7)

= 1 - P(z < 0.23)

= 1 - 0.5910 Using standard normal table.

= 0.4090

Probability = 0.4090