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The problem is asking to determine the proportion of male babies who weigh more than 12 pounds, given that their weights are normally distributed with a mean of 11.6 pounds and a standard deviation of 2.9 pounds. The solution involves calculating the area under the normal distribution curve to the right of 12 pounds.

### Solution Process:
1. **Standardize the value of 12 pounds**: We need to convert 12 pounds into a z-score using the formula:
   \[
   z = \frac{x - \mu}{\sigma}
   \]
   where:
   - \(x = 12\) (the value we're interested in),
   - \(\mu = 11.6\) (the mean),
   - \(\sigma = 2.9\) (the standard deviation).

   Substituting the values:
   \[
   z = \frac{12 - 11.6}{2.9} = \frac{0.4}{2.9} \approx 0.1379
   \]

2. **Use the z-table or calculator**: Now, using the z-score of approximately 0.1379, find the area to the right of this z-score (since we want the proportion weighing more than 12 pounds). The z-table gives the cumulative area to the left of the z-score.

   For \(z = 0.1379\), the cumulative probability from a standard normal distribution table is around 0.5548. Therefore, the area to the right (i.e., the proportion of babies weighing more than 12 pounds) is:
   \[
   1 - 0.5548 = 0.4452
   \]

So, the correct proportion should be approximately **0.4452**, not **0.3061** as shown in the input.

Would you like further details on the calculations or clarification on any part? 

Here are some related questions to expand understanding:
1. What is the z-score for a baby weighing exactly 11.6 pounds?
2. How would the proportion change if the mean were 12 pounds instead of 11.6 pounds?
3. What is the probability of a baby weighing less than 10 pounds?
4. How can you interpret the standard deviation in the context of baby weights?
5. How would you calculate the probability of a baby weighing between 10 and 13 pounds?

**Tip**: Always double-check the z-score and corresponding areas using a z-table or calculator for precision in normal distribution problems.

What proportion of babies weigh more than 12 pounds?

Learn how to calculate the proportion of male babies who weigh more than 12 pounds using the normal distribution. This problem uses a mean of 11.6 pounds, a standard deviation of 2.9 pounds, and z-scores to determine the proportion.

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