Suppose a battery has a useful life described by the exponential distribution with a mean of 500 days. a) What is the probability that it will fail before its expected lifetime?b) What is the probability that it will not fail within the first year?c) What is the probability that a battery which has lasted 365 days will operate beyond its expected lifetime? (Use Markov’s property)d) What is the median amount of days the battery will last?

Mean=500 days X is the exponential distribution with mean= 500 days

Answered: Suppose a battery has a useful life…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 19E

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Suppose a battery has a useful life described by the exponential distribution with a mean of 500 days.

a) What is the probability that it will fail before its expected lifetime?
b) What is the probability that it will not fail within the first year?
c) What is the probability that a battery which has lasted 365 days will operate beyond its expected lifetime? (Use Markov’s property)
d) What is the median amount of days the battery will last?

Definition Definition Middle value of a data set. The median divides a data set into two halves, and it also called the 50th percentile. The median is much less affected by outliers and skewed data than the mean. If the number of elements in a dataset is odd, then the middlemost element of the data arranged in ascending or descending order is the median. If the number of elements in the dataset is even, the average of the two central elements of the arranged data is the median of the set. For example, if a dataset has five items—12, 13, 21, 27, 31—the median is the third item in ascending order, or 21. If a dataset has six items—12, 13, 21, 27, 31, 33—the median is the average of the third (21) and fourth (27) items. It is calculated as follows: (21 + 27) / 2 = 24.

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