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Solution:
\n" ); document.write( "The birth weights for twins are normally distributed with a mean ($\mu$) of 2350 grams and a standard deviation ($\sigma$) of 645 grams. We want to determine if a birth weight of 2255 grams could be considered unusual.\r
\n" ); document.write( "\n" ); document.write( "To do this, we first calculate the z-score for a birth weight of 2255 grams using the formula:
\n" ); document.write( "$z = \frac{x - \mu}{\sigma}$
\n" ); document.write( "where $x$ is the birth weight, $\mu$ is the mean birth weight, and $\sigma$ is the standard deviation.\r
\n" ); document.write( "\n" ); document.write( "Given:
\n" ); document.write( "$x = 2255$ grams
\n" ); document.write( "$\mu = 2350$ grams
\n" ); document.write( "$\sigma = 645$ grams\r
\n" ); document.write( "\n" ); document.write( "Calculate the z-score:
\n" ); document.write( "$z = \frac{2255 - 2350}{645} = \frac{-95}{645} \approx -0.147$\r
\n" ); document.write( "\n" ); document.write( "Rounding the z-score to two decimal places, we get $z \approx -0.15$.\r
\n" ); document.write( "\n" ); document.write( "Now, we need to determine if this z-score indicates an unusual birth weight. A common rule of thumb is that a data point is considered unusual if its z-score is less than -2 or greater than 2. This corresponds to data points that are more than 2 standard deviations away from the mean.\r
\n" ); document.write( "\n" ); document.write( "In this case, the z-score of -0.15 is between -2 and 2. Therefore, a birth weight of 2255 grams is not considered unusual based on this criterion. It falls within the typical range of birth weights for twins according to the given distribution.\r
\n" ); document.write( "\n" ); document.write( "Final Answer: The final answer is $\boxed{z \approx -0.15, \text{ not unusual}}$ \n" ); document.write( "