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) ?

Question

Leon

Mathematics

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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Isabelle · Answer 1

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.