Asked Oct 16, 2019


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.



Expert Answer

Step 1


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:


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Step 2

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


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950 1000 <Z< 800 1000 P(800X950) = P| 100 100 P(-2.00< Z<-0.50) - P(Z<-0.50)-P(Z <-2.00) 0.3085- 0.0228 0.2857


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