The shelf life of a battery produced by one major company is known to be normally distributed with a mean life of 9 years and a standard dev

Question

The shelf life of a battery produced by one major company is known to be normally distributed with a mean life of 9 years and a standard deviation of 0.2 years. What value of shelf life do 16% of the battery shelf lives fall below.What value of shelf life do 16% of the battery shelf lives fall above? Round your answer to one decimal place.

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Vivian 2 weeks 2021-09-09T17:26:10+00:00 1 Answer 0

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    2021-09-09T17:27:30+00:00

    Answer: the value of shell life is 9.2 hours.

    Step-by-step explanation:

    Since the shelf life of a battery produced by one major company is known to be normally distributed, we would apply the formula for normal distribution which is expressed as

    z = (x – µ)/σ

    Where

    x = shelf life of a batteries in years.

    µ = mean shell life

    σ = standard deviation

    From the information given,

    µ = 9 years

    σ = 0.2 years

    Looking at the normal distribution table, the z score corresponding to the p value of 16%(16/100 = 0.16) is – 0.9. Therefore

    – 0.9 = (x – 9)/0.2

    0.2 × – 0.9 = x – 9

    0.18 = x – 9

    x = 0.18 + 9

    x = 9.2

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