A type of battery-operated led lights has a known mean lifetime 7.9 hours with standard deviation 0.5. Assuming that the lifetimes of these

Question

A type of battery-operated led lights has a known mean lifetime 7.9 hours with standard deviation 0.5. Assuming that the lifetimes of these led lights have a nearly symmetric/bell-curve distribution, find the percent (%) of these led lights having lifetime between 7.9 and 8.9 hours.

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Hải Đăng 4 years 2021-07-20T19:39:06+00:00 1 Answers 18 views 0

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  1. diemkieu
    0
    2021-07-20T19:40:42+00:00
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    Answer:

    47.5% of these led lights have lifetime between 7.9 and 8.9 hours.

    Step-by-step explanation:

    The Empirical Rule states that, for a normally distributed random variable:

    68% of the measures are within 1 standard deviation of the mean.

    95% of the measures are within 2 standard deviation of the mean.

    99.7% of the measures are within 3 standard deviations of the mean.

    In this problem, we have that:

    Mean = 7.9 hours

    Standard deviation = 0.5 hours

    The normal distribution is symmetric, which means that 50% of the measures are below the mean and 50% are above.

    Lifetime between 7.9 and 8.9 hours:

    7.9 hours is the mean.

    8.9 = 7.9 + 2*0.5

    So 8.9 hours is two standard deviations above the mean.

    Of the 50% of the measures that are above the mean, 95% are between the mean of 7.9 and two standard deviations above the mean(8.9). So

    0.5*0.95 = 0.475

    47.5% of these led lights have lifetime between 7.9 and 8.9 hours.

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