Questions: The accompanying table describes results from groups of 10 births from 10 different sets of parents. The random variable x represents the number of girls among 10 children. Use the range rule of thumb to determine whether 1 girl in 10 births is a significantly low number of girls. Use the range rule of thumb to identify a range of values that are not significant. The maximum value in this range is 8.5 girls. (Round to one decimal place as needed.) The minimum value in this range is 1.5 girls. (Round to one decimal place as needed.) Based on the result, is 1 girl in 10 births a significantly low number of girls? Explain. A. Yes, 1 girl is a significantly low number of girls, because 1 girl is below the range of values that are not significant. B. No. 1 girl is not a significantly low number of girls, because 1 girl is within the range of values that are not significant. C. Yes. 1 girl is a significantly low number of girls, because 1 girl is above the range of values that are not significant. D. Not enough information is given.

The accompanying table describes results from groups of 10 births from 10 different sets of parents. The random variable x represents the number of girls among 10 children. Use the range rule of thumb to determine whether 1 girl in 10 births is a significantly low number of girls. Use the range rule of thumb to identify a range of values that are not significant. The maximum value in this range is 8.5 girls. (Round to one decimal place as needed.) The minimum value in this range is 1.5 girls. (Round to one decimal place as needed.) Based on the result, is 1 girl in 10 births a significantly low number of girls? Explain. A. Yes, 1 girl is a significantly low number of girls, because 1 girl is below the range of values that are not significant. B. No. 1 girl is not a significantly low number of girls, because 1 girl is within the range of values that are not significant. C. Yes. 1 girl is a significantly low number of girls, because 1 girl is above the range of values that are not significant. D. Not enough information is given.
Transcript text: The accompanying table describes results from groups of 10 births from 10 different sets of parents. The random variable $x$ represents the number of girls among 10 children. Use the range rule of thumb to determine whether 1 girl in 10 births is a significantly low number of girls. Use the range rule of thumb to identify a range of values that are not significant. The maximum value in this range is 8.5 girls. (Round to one decimal place as needed.) The minimum value in this range is 1.5 girls. (Round to one decimal place as needed.) Based on the result, is 1 girl in 10 births a significantly low number of girls? Explain. A. Yes, 1 girl is a significantly low number of girls, because 1 girl is below the range of values that are not significant. B. No. 1 girl is not a significantly low number of girls, because 1 girl is within the range of values that are not significant. C. Yes. 1 girl is a significantly low number of girls, because 1 girl is above the range of values that are not significant. D. Not enough information is given.
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Solution

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Solution Steps

Step 1: Calculate the Mean

The mean \( \mu \) of the number of girls in 10 births is calculated as follows:

\[ \mu = \frac{\sum_{i=1}^N x_i}{N} = \frac{55}{10} = 5.5 \]

Step 2: Calculate the Variance and Standard Deviation

The variance \( \sigma^2 \) is calculated using the formula:

\[ \sigma^2 = \frac{\sum (x_i - \mu)^2}{n} = 8.2 \]

The standard deviation \( \sigma \) is then obtained by taking the square root of the variance:

\[ \sigma = \sqrt{8.2} \approx 2.9 \]

Step 3: Determine the Range of Non-Significant Values

Using the range rule of thumb, we calculate the range of non-significant values as follows:

\[ \text{Range} = \mu \pm 2\sigma \]

Calculating the minimum and maximum values:

\[ \text{Minimum} = 5.5 - 2 \times 2.9 \approx -0.3 \] \[ \text{Maximum} = 5.5 + 2 \times 2.9 \approx 11.3 \]

Thus, the range of non-significant values is approximately \([-0.3, 11.3]\).

Step 4: Assess Significance of 1 Girl

To determine if having 1 girl is significantly low, we check if 1 is within the range of non-significant values:

Since \( 1 > -0.3 \) and \( 1 < 11.3 \), we conclude that 1 girl is not a significantly low number of girls.

Final Answer

The answer is B.

\(\boxed{B}\)

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