An electrical firm manufactures light bulbs that have a length life with normal distribution, and mean equal to 800 hours, and a variance of 9. Find the probability that a random sample of 21 light bulbs will have a sample variance S² between 6.56 and 11.27.

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A: this is matrix question  apply matrix subtraction operation, you get result

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Q: a) : ?

A: here differentiate both sides with respect to x.

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A: The explanation of answer as follows

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A: The given equations,x-y=2x=-2

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A: We have to calculate ϕ(23)

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A: Image is attached with detailed solution.

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A: Given,           y'=x+1y4+1

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A: .

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A: Cartesian product of c, d and c, d isc, c, c, d, d, c, d, d Further,           c, d× c, c, c, d, d,…