The life of a light bulb is exponentially distributed with a mean of 1,000 hours. What is the probability that the bulb will last less than 800 hours?
Accepted Solution
A:
Answer: 0.5507Step-by-step explanation:The cumulative distribution function for exponential distribution:-[tex]P(X\leq x)=1-e^{-\lambda x}[/tex]Given : The life of a light bulb is exponentially distributed with a mean of 1,000 hours. Then , [tex]\lambda=\dfrac{1}{1000}[/tex]Then , the probability that the bulb will last less than 800 hours is given by :-[tex]P(X\leq 800)=1-e^{\frac{-800}{1000}}\\\\=1-e^{-0.8}=0.5506710358\approx0.5507[/tex]Hence, the probability that the bulb will last less than 800 hours = 0.5507