Suppose the amount of time that a certain battery functions is a normal random variable with a mean 400 and a standard deviation of 40 hours. (Note that sum of two independent normal random variables is normal with mean equal to the sum of the two means and variance equal to the sum of the two variances.) The probability that the total life of two batteries will exceed 760 hours is given by 0.2389 0.7611 0.2611 0.341

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Suppose the amount of time that a certain battery functions is a normal random variable with a mean 400 and a standard deviation of 40 hours. (Note that sum of two independent normal random variables is normal with mean equal to the sum of the two means and variance equal to the sum of the two variances.) The probability that the total life of two batteries will exceed 760 hours is given by 0.2389 0.7611 0.2611 0.3413
Expert Solution
Step 1

Given:

Population mean time μ=400

Population standard deviation σ=40

Xi ~N (400, 402)

X1 be the life of first battery

X2 be the life of second battery

T be the total batter life.

T = X1 + X2

T~N400+400, 402+402T~N800, 3200

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