The life span of an electrical component has the, Basic Statistics

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The life span of an electrical component has the

Question: The life span of an electrical component has the exponential distribution with parameter λ = 0.013. Let X₁, ... , X₁₀₀be a simple random sample of 100 life times of such components.

(a) What will be the approximate value of their average X¯?

(b) What can be said about the probability that X¯ will be within 15.38 units from the population mean? (Hint. The mean and variance of a random variable having the exponential distribution with parameter λ are 1/λ and 1/λ², respectively.)

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