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 calculate the indefinite integral of the given probability density function and evaluate it from 0 to 10 minutes:

∫(1/30e^(-t/30))dt = (-e^(-t/30)) + C

Using the limits:

P(response time ≤ 10) = ∫0^10 (1/30e^(-t/30))dt = (-e^(-10/30)) - (-e^0) = 0.391

Therefore, the answer is C.

Suppose in a Small City the Response Time T (In