The lifespan of an electrical component has an exponential distribution with parameter lambda = 0.013. Suppose...

The lifespan of an electrical component has an exponential distribution with parameter lambda = 0.013. Suppose we have an iid sample of size 100 of these components

Some hints: P(X < c) for an exponential(lambda) can be found via pexp(c,lambda) E[X] = 1/lambda and Var[X] = 1/lambda^2

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Using the exact probability distribution, what is the probability that a single component will be within 15.38 units of the population mean?

Using Chebyshev's inequality, what is a lower bound on the probability that the sample mean will be within 15.38 units of the population mean?

Using the CLT, what is an approximation to the probability that the sample mean will be within 15.38 units of the population mean?

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orchestra answered 1 year ago

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