Question

The response time of a fire department in an emergency call is the period between the time the call
is received by the dispatcher and the time the first truck service arrives on the scene. It was found
that the response time follows a normal distribution with mean of 12 min and standard deviation of
2 min.
a) What is the probability that the response time is less than 15 min?
b) A dispatcher claims that the response time exceeds 10 min in at least 90% of cases. Is his
assertion true? Justify your answer.

Answer 1

Let X denotes the response time.

X ~ Normal(12, 2²)

a) The probability that the response time is less than 15 min

b)

, so his assertion is not true.