The lifetimes of a certain type of calculator battery are normally distributed. The mean lifetime is 400 days, with a standard deviation of

Question

The lifetimes of a certain type of calculator battery are normally distributed. The mean lifetime is 400 days, with a standard deviation of 50 days. For a sample of 6000 new batteries, determine how many batteries will last:

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Nho 4 years 2021-08-14T22:14:32+00:00 1 Answers 185 views 0

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  1. niczorrrr
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    2021-08-14T22:16:08+00:00
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    Complete question :

    The lifetimes of a certain type of calculator battery are normally distributed. The mean lifetime is 400 days, with a standard deviation of 50 days. For a sample of 6000 new batteries, determine how many batteries will last: 360 and 460 days

    Answer:

    0.67307

    Step-by-step explanation:

    Given that :

    Mean, m = 400

    Standard deviation, s = 50

    Sample size, n = 6000

    Obtain the standardized score :

    Zscore =(x – m) / s

    For X = 360

    P(x < 360)

    Zscore =(360 – 400) / 50

    Zscore = – 40 / 50

    Zscore = – 0.8

    P(Z < – 0.8) = 0.21186

    For X = 460

    P(x < 460)

    Zscore =(460 – 400) / 50

    Zscore = 60 / 50

    Zscore = 1.2

    P(Z < 1.2) = 0.88493

    P(Z < 1.2) – P(Z < – 0.8)

    0.88493 – 0.21186

    = 0.67307

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