# The lifetime of a particular component is normally distributed with a mean of 1000 hours and a standard deviation of 100 hours. Find the probability that a randomly drawn component will last between 800 and 950 hours.

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The lifetime of a particular component is normally distributed with a mean of 1000 hours and a standard deviation of 100 hours. Find the probability that a randomly drawn component will last between 800 and 950 hours.

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Step 1

Introduction:

Let X denotes the lifetime of a particular component is normally distributed with mean of 1000 hours and standard deviation 100 hours. Here, X ~ N (μ = 1000, σ = 100).

Let X ~ N (μ, σ), then the standard z-score is found using the formula given below:

Step 2

The probability that all component are between 800 an...

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