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 24 minutes, what is the probability that X is less than 32 minutes? (Do not round until the final step. Round your answer to 3 decimal places.)

Answer 1

Answer:

The probability that X is less than 32 minutes is 0.736.

Step-by-step explanation:

Given : 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 24 minutes.

To find : What is the probability that X is less than 32 minutes?

Solution :

If X has an average value of 24 minutes.

i.e. $\lambda=24$

The random variable X is exponentially distributed, where X represents the time it takes for a person to choose a birthday gift.

The exponentially function is $\frac{1}{\lambda}e^{-\frac{x}{\lambda}}$

The function form according to question is

$f(x)=\{\frac{1}{24}e^{-\frac{x}{24}}, x>0\}$

The probability that X is less than 32 minutes is

$P[x$

$P[x$

$P[x$

Therefore, the probability that X is less than 32 minutes is 0.736.