**Understanding Battery Life and Probability**The length of life (in days) of an alkaline battery follows an exponential distribution, which is a common way to model the time between events in a process that occurs continuously and independently at a constant average rate. In this scenario, the average life of the battery is 1 year. Thus, the rate parameter \(\lambda\) (lambda) is \(\frac{1}{365}\).**Problem Statement:**(a) What is the probability that an alkaline battery will fail before 185 days?To approach this, one would typically use the exponential distribution formula for the probability of failure before a certain time \(t\):\[ P(T < t) = 1 - e^{-\lambda t} \]Where:- \( P(T < t) \) is the probability that the battery life is less than \(t\) days,- \(\lambda\) is the rate parameter, here given as \(\frac{1}{365}\),- \(t\) is the time in days before which we want to find the probability of failure, i.e., 185 days in this case.Be sure to round your final answer to four decimal places as specified.

Answered: 1 The length of life (in days) of an…

MATLAB: An Introduction with Applications

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ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

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1 The length of life (in days) of an alkaline battery has an exponential distribution with an average life of 1 year, so that λ = 365 (a) What is the probability that an alkaline battery will fail before 185 days? X (Round your answers to four decimal places.)