According to the empirical rule, 68% of all newborn babies in the United States weigh between 3000 g and 4000 g.
What is empirical rule?
According to the empirical rule, also known as 68-95-99.7 rule, the percentage of values that lie within an interval with 68%, 95% and 99.7% of the values lies within one, two or three standard deviations of the mean of the distribution.
[tex]P(\mu - \sigma < X < \mu + \sigma) = 68\%\\P(\mu - 2\sigma < X < \mu + 2\sigma) = 95\%\\P(\mu - 3\sigma < X < \mu + 3\sigma) = 99.7\%[/tex]
Here, mean of distribution of X is [tex]\mu[/tex] and standard deviation from mean of distribution of X is [tex]\sigma[/tex]
In the United States, birth weights of newborn babies are approximately normally distributed with a mean of
[tex]\mu = 3,500\rm \;g[/tex]
The standard deviation of the babies is,
[tex]\sigma = 500 g[/tex]
Put the value in the empirical formula for 68% as,
[tex]P(3500-500 < X < 3500+ 500) = 68\%\\P(3000 < X < 4000) = 68\%[/tex]
Hence, according to the empirical rule, 68% of all newborn babies in the United States weigh between 3000 g and 4000 g.
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