Answer:
0.674
Step-by-step explanation:
If the random variable X is exponentially distributed and X has an average value of 25 minutes, then its probability density function (PDF) is
[tex] \bf f(x)=\frac{1}{25}e^{-x/25}\;(x\geq 0)[/tex]
and its cumulative distribution function (CDF) is
[tex] \bf P(X\leq t)=\int_{0}^{t} f(x)dx=1-e^{-t/25}[/tex]
So, the probability that X is less than 28 minutes is
[tex] \bf P(X\leq 28)=1-e^{-28/25}=1-e^{-1.12}=0.674[/tex]
