Question

Your company's new series "Avocado Comedy Hour" has been a complete flop, with viewership continuously declining at a rate of 28% per month. Use a suitable density function to calculate the probability that a randomly chosen viewer will be lost sometime in the next three months. (Round your answer to four decimal places.)

Answer 1

Answer:

The probability that a viewer will be lost sometime in the next three months is 0.5683

Step-by-step explanation:

The probability density function that you need to use is the exponential density function because in the problem says that viewership is continuously declining at a rate of 28% per month.

An exponential density function is a function of the form:

$f(x)=ae^{-ax}$ where a a positive constant and is known as rate parameter.

To find that the probability that a randomly chosen viewer will be lost sometime in the next three months you use this

$P(0\leq X\leq 3)=\int\limits^3_0 {0.28e^{-0.28x} } \, dx \\ P(0\leq X\leq 3)=-e^{-0.28*3}+e^{-0.28*0} = 0.5683$