To determine whether 1 girl in 10 births is a significantly low number, we will apply the "range rule of thumb." According to this rule, values are considered significantly low or high if they fall more than 2 standard deviations from the mean.

Steps:

1. Calculate the mean (expected value): The mean, $\mu$, of a probability distribution is calculated using: $\mu = \sum \left( x \times P(x) \right)$ where $x$ is the number of girls and $P(x)$ is the probability associated with $x$.

2. Calculate the standard deviation: The standard deviation, $\sigma$, is given by: $\sigma = \sqrt{\sum \left( (x - \mu)^2 \times P(x) \right)}$

3. Determine the range of non-significant values: Using the range rule of thumb: $\text{Lower bound} = \mu - 2\sigma$ $\text{Upper bound} = \mu + 2\sigma$

Let's start by calculating the mean and standard deviation from the table data.

Step 1: Mean Calculation

We calculate $\mu$ using the following formula: $\mu = (0 \times 0.005) + (1 \times 0.016) + (2 \times 0.042) + \dots + (10 \times 0.016)$

Step 2: Standard Deviation Calculation

Next, we'll calculate the variance: $\sigma^2 = \sum (x - \mu)^2 \times P(x)$ And then, take the square root to get $\sigma$.

I'll now proceed with these calculations to get the mean, standard deviation, and the range of values that are not considered significant.

Let me calculate that for you.### Results:

1. Mean (Expected value): $\mu = 5.06$ (rounded to two decimal places)
2. Standard deviation: $\sigma = 1.74$ (rounded to two decimal places)
3. Range of non-significant values: $\text{Lower bound} = 1.57$ $\text{Upper bound} = 8.54$

Conclusion:

According to the range rule of thumb, the number of girls that would not be considered significant lies between approximately 1.57 and 8.54. Since 1 girl falls below the lower bound of 1.57, it can be considered significantly low.

Would you like more details on any of these steps or any clarifications?

Related Questions:

1. How is the range rule of thumb applied in other distributions?
2. What does a significantly high number of girls in 10 births look like?
3. How do mean and standard deviation affect the significance of a value?
4. What other methods can be used to determine significant deviations in probability?
5. How does the binomial distribution relate to this problem?

Tip: Always double-check that the sum of probabilities adds up to 1 in a probability distribution to ensure accuracy!