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

To determine if 1 girl in 10 births is a significantly low number of girls, we can use the **range rule of thumb**. This rule helps us to identify whether a value is significantly low or high by determining if it falls below a certain lower threshold or above a certain upper threshold. Here's the step-by-step process:

### Step 1: Mean (μ) of the Random Variable \( x \)

In this case, the random variable \( x \) represents the number of girls among 10 children. We can assume that the probability of having a girl in each birth is 0.5 (since boys and girls are equally likely).

The mean \( \mu \) of a binomial distribution is calculated using the formula:
\[
\mu = n \times p
\]
Where:
- \( n = 10 \) (the number of trials, i.e., 10 births),
- \( p = 0.5 \) (the probability of having a girl).

\[
\mu = 10 \times 0.5 = 5
\]
Thus, the mean number of girls is 5.

### Step 2: Standard Deviation (σ)

The standard deviation \( \sigma \) of a binomial distribution is calculated using the formula:
\[
\sigma = \sqrt{n \times p \times (1 - p)}
\]
Where:
- \( n = 10 \),
- \( p = 0.5 \),
- \( 1 - p = 0.5 \) (since the probability of a boy is also 0.5).

\[
\sigma = \sqrt{10 \times 0.5 \times 0.5} = \sqrt{2.5}

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.

Learn how to determine whether 1 girl in 10 births is a significantly low number using the range rule of thumb. This problem covers binomial distribution, probability, and key statistical formulas such as mean and standard deviation. Suitable for students in Grades 9-12.

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