# In order to stay alert at work, an employee set a timer to go off randomly sometime within 40 minutes. What is the probability the timer will go off between minutes 20 to 35?

In order to stay alert at work, an employee set a timer to go off randomly sometime within 40 minutes. What is the probability the timer will go off between minutes 20 to 35?
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Kailey Santana
Time to which the timer will go off is uniformly distributed from a = 0 minutes and b = 40 minutes
Probability that the timer will go off between ${x}_{1}=20$ minutes and ${x}_{2}=35$ minutes is $\frac{\left({x}_{2}-{x}_{1}\right)}{\left(b-a\right)}$
$=\frac{\left(35-20\right)}{\left(40-0\right)}$
$=0.375$