Question

The random variable X is exponentially distributed, where X represents the time it takes for a person to choose a birthday gift. If X has an average value of 25 minutes, what is the probability that X is less than 28 minutes? (Do not round until the final step. Round your answer to 3 decimal places.)

Answer 1

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

$\bf f(x)=\frac{1}{25}e^{-x/25}\;(x\geq 0)$

and its cumulative distribution function (CDF) is

$\bf P(X\leq t)=\int_{0}^{t} f(x)dx=1-e^{-t/25}$

So, the probability that X is less than 28 minutes is

$\bf P(X\leq 28)=1-e^{-28/25}=1-e^{-1.12}=0.674$