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25 August, 18:24

A sleep time of 15.9 hours per day for a newborn baby is at the 10th percentile of the distribution of sleep times for all newborn babies. Assuming the distribution is normal with standard deviation 0.5 hour, approximately what is the mean sleep time, in hours per day, for newborn babies?

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  1. 25 August, 20:58
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    The mean sleep time is 16.54 hours per day for newborn babies

    Explanation:

    * Lets explain how to solve the problem

    Percentiles are used to compare data across a larger sample.

    To calculate the percentile, you will need to know the score, the mean

    and the standard deviation.

    In the problem you have the percentile and you want to find the mean.

    To do that we must find z-score for the percentile from the normal

    distribution table.

    If the percentile lower than the 50th percentile, you will get a negative

    z-score.

    z-score = (x - μ) / σ, where x is the score, μ is the mean and σ is the

    standard deviation

    A sleep time of 15.9 hours per day for a newborn baby

    x = 15.9 hours

    At the 10th percentile of the distribution of sleep times for all newborn

    babies

    That means we want to find z-score corresponding to 0.1 (10/100 = 0.1)

    By using the normal distribution table

    z = - 1.28

    The standard deviation is 0.5 hour

    σ = 0.5

    Substitute these values in the rule above

    -1.28 = (15.9 - μ) / 0.5

    Multiply both sides by 0.5

    -0.64 = 15.9 - μ

    Add μ to both sides

    -0.64 + μ = 15.9

    add - 0.64 to both sides

    μ = 15.9 + 0.64 = 16.54

    The mean sleep time is 16.54 hours per day for newborn babies
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