Answer: 0.1342
Step-by-step explanation:
The cumulative distribution function for exponential distribution is :-
[tex]P(x)=1-e^{\frac{-x}{\lambda}}[/tex], where [tex]\lambda [/tex] is the mean of the distribution.
Given : [tex]\lambda =20[/tex]
Then , the probability that the battery will last between 10 and 15 hours is given by :-
[tex]P(10<x<15)=P(15)-P(10)\\\\=1-e^{\frac{-15}{20}}-(1-e^{\frac{-10}{20}})\\\\=-e^{-0.75}+e^{-0.5}=0.13416410697\approx0.1342[/tex]
Hence, the probability that the battery will last between 10 and 15 hours = 0.1342
