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12 February, 06:22

The infant mortality rate (per 1,000 live births) for the 50 states and the District of Columbia has a mean of 6.98 and a standard deviation of 1.62. Assuming that the distribution is normal, what percentage of states have an infant mortality rate between 5.36 and 8.60 percent (per 1,000 live births) ?

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  1. 12 February, 06:47
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    68% of states have an infant mortality rate between 5.36 and 8.60 percent.

    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 = 6.98

    Standard deviation = 1.62

    Assuming that the distribution is normal, what percentage of states have an infant mortality rate between 5.36 and 8.60 percent (per 1,000 live births) ?

    5.36 = 6.98 - 1*1.62

    So 5.36 is one standard deviation below the mean

    8.60 = 6.98 + 1*1.62

    So 8.60 is one standard deviation above the mean

    By the Empirical Rule, 68% of states have an infant mortality rate between 5.36 and 8.60 percent.
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