Answer:
The probability is

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
⇒
