Your school wants to test the fire alarm system during the two hour period between 9:00 a. M. And 11:00 a. M. The probability of testing the fire alarm during this period is uniformly distributed that is X∼U(0,120). Find the probability that you have to wait more than 30 minutes, that is, find P(X>30).

The probability is

Step-by-step explanation:

We know that the probability of testing the fire alarm during this period is uniformly distributed that is ~ .

We need to find

Given a continuous random variable with distribution :

~ , where '''' and '''' are real numbers

The probability density function is :

   if x ∈ (a,b)

 if x ∉ (a,b)

In the exercise we have ~ , therefore the probability density function is :

if x ∈ (0,120)

if x ∉ (0,120)

If we want to find we need to perform the integral

Where and '''' represents + ∞

Now, given that is 0 when x ∉ (0,120), we will need to integrate between 30 and 120 to find the probability.

If we perform this integral ⇒

Where and ⇒

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