The birth weights of 50,000 babies were recorded and analyzed. The distribution of the data is normal. Which portion of the data is less than the mean?

Rationale

50% of the data is less than the mean.

In a normal distribution, the mean is the central point, which divides the data into two equal halves. Therefore, exactly half of the data falls below the mean, making the portion less than the mean 50%.

A (50%) CORRECT

This choice accurately represents the property of a normal distribution where the mean divides the data into two equal parts. Thus, 50% of the recorded birth weights are below the mean, affirming that this is the correct answer.

B (68%) YOUR ANSWER

This percentage refers to the empirical rule, which states that approximately 68% of the data falls within one standard deviation of the mean in a normal distribution. However, it does not indicate the portion of data less than the mean, as it encompasses both sides of the mean.

C (95%) YOUR ANSWER

Similar to option B, this percentage pertains to the empirical rule, which states that about 95% of the data lies within two standard deviations of the mean. This value does not represent the portion of data less than the mean but rather the larger range of values around it.

D (99.70%) YOUR ANSWER

This choice indicates the proportion of data within three standard deviations of the mean, according to the empirical rule. While it shows a broader range of values, it does not specify the portion of data below the mean, which remains at 50%.

Conclusion

In a normal distribution, the mean acts as a dividing line, with exactly 50% of the data falling below it. Understanding this property is crucial for interpreting statistical data, as it illustrates the balance within the distribution. Other percentages, such as 68%, 95%, and 99.70%, refer to ranges rather than the specific portion below the mean, thereby highlighting the significance of recognizing the mean's role in data analysis.

The birth weights of 50,000 babies were recorded and analyzed. The distribution of the data is normal. Which portion of the data is less than the mean?

50% of the data is less than the mean.

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