Answer:
The probability is 0.4972
Step-by-step explanation:
The probability density function for the time of failure is:
f(t) = k e^(-kt)
Where k=1/a and a = 80hr so f(t) is equal to:
[tex]f(t)=\frac{1}{a}e^{\frac{-t}{a} }[/tex]
[tex]f(t)=\frac{1}{80}e^{\frac{-t}{80} }[/tex]
Then, if the probability density function follow a exponential distribution, the probability distribution function is:
[tex]F(t)=1-e^{-t/a}[/tex]
[tex]F(t)=1-e^{-t/80}[/tex]
The probability distribution function give as the probability that a failure will occur in t hours or less, so the probability that a failure will occur in 55 hr or less is calculated as:
[tex]F(55)=1-e^{-55/80}=0.4972[/tex]
