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:The probability that a viewer will be lost sometime in the next three months is 0.5683Step-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:[tex]f(x)=ae^{-ax}[/tex] 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[tex]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[/tex]