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19 February, 23:59

The lifetime of a 2-volt non-rechargeable battery in constant use has a normal distribution with a mean of 516 hours and a standard deviation of 20 hours. Ninety percent of all batteries have a lifetime less than

A. 517.28 hours

B. 536. 00 hours

C. 541.60 hours

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Answers (1)
  1. 20 February, 01:00
    0
    Answer: C. 541.60 hours

    Step-by-step explanation:

    Since the lifetime of a 2-volt non-rechargeable battery in constant use has a normal distribution, we would apply the formula for normal distribution which is expressed as

    z = (x - µ) / σ

    Where

    x = lifetime of the batteries.

    µ = mean lifetime

    σ = standard deviation

    From the information given,

    µ = 516 hours

    σ = 20 hours

    Looking at the normal distribution table, the z score corresponding to ninety percent approximately is 1.28

    Therefore,

    1.28 = (x - 516) / 20

    Cross multiplying by 20, it becomes

    20 * 1.28 = x - 516

    25.6 = x - 516

    x = 516 + 25.6

    x = 541.6

    Therefore, Ninety percent of all batteries have a lifetime less than

    541.60 hours
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