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In the United States, birth weights of newborn babies are approximately normally distributed with a mean of [tex]\mu=3,500 \, \text{g}[/tex] and a standard deviation of [tex]\sigma=500 \, \text{g}[/tex].

According to the empirical rule, [tex]68 \%[/tex] of all newborn babies in the United States weigh between [tex]3,000 \, \text{g}[/tex] and [tex]4,000 \, \text{g}[/tex].



Answer :

GinnyAnswer
To determine the range within which 68% of all newborn babies in the United States weigh, we use the empirical rule (also known as the 68-95-99.7 rule) which applies to normally distributed data.

The empirical rule states the following:
- Approximately 68% of the data falls within one standard deviation from the mean.
- Approximately 95% of the data falls within two standard deviations from the mean.
- Approximately 99.7% of the data falls within three standard deviations from the mean.

Given the data:
- Mean birth weight, [tex]\(\mu = 3,500 \text{ g}\)[/tex]
- Standard deviation, [tex]\(\sigma = 500 \text{ g}\)[/tex]

For 68% of the data to lie within one standard deviation from the mean, we need to calculate the range that falls within [tex]\(\mu - \sigma\)[/tex] to [tex]\(\mu + \sigma\)[/tex].

Step-by-step solution:

1. Calculate the lower bound:
[tex]\[ \text{Lower bound} = \mu - \sigma = 3500 \text{ g} - 500 \text{ g} = 3000 \text{ g} \][/tex]

2. Calculate the upper bound:
[tex]\[ \text{Upper bound} = \mu + \sigma = 3500 \text{ g} + 500 \text{ g} = 4000 \text{ g} \][/tex]

Therefore, according to the empirical rule, 68% of all newborn babies in the United States weigh between [tex]\(\boxed{3000 \text{ g}}\)[/tex] and [tex]\(\boxed{4000 \text{ g}}\)[/tex].