Suppose in a small city the response time t (in minutes) of the fire company is given by the probability density function . For a fire chosen at random, find the probability that the response time is 10 minutes or less. Round your answer to three decimal places.
A) 0.242
B) 0.567
C) 0.391
D) 0.758
E) 0.609

Question

Suppose in a small city the response time t (in minutes) of the fire company is given by the probability density function  . For a fire chosen at random, find the probability that the response time is 10 minutes or less. Round your answer to three decimal places. ​
A) 0.242 
B) 0.567 
C) 0.391 
D) 0.758 
E) 0.609

Quizplus · Accepted Answer

We need to find the probability P(T ≤ 10).

We can use the cumulative distribution function (CDF) to calculate this probability:

F(10) = ∫₀¹₀ f(t) dt

Using the given probability density function, we have:

F(10) = ∫₀¹₀ 0.02e^(-0.02t) dt

Integrating using integration by substitution (let u = 0.02t, du = 0.02 dt), we get:

F(10) = [-e^(-0.02t)]₀¹₀

F(10) = -e^(-0.2) + 1

F(10) ≈ 0.391

Therefore, the probability that the response time is 10 minutes or less is 0.391. The best choice is C.

Suppose in a Small City the Response Time T (In