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Let's solve the questions based on the probability distribution table provided in the image:

### Table Information:
- The number of girls, \( x \), in 10 births is listed with their corresponding probabilities, \( P(x) \).

### a) What is the probability of exactly 8 girls in 10 births?
From the table:
- \( P(8) = 0.043945 \).

So, the probability of exactly 8 girls in 10 births is **0.043945**.

---

### b) What is the probability of 8 or more girls in 10 births?
This is the sum of the probabilities for 8, 9, and 10 girls:
\[
P(8 \text{ or more}) = P(8) + P(9) + P(10)
\]
From the table:
\[
P(8) = 0.043945, \quad P(9) = 0.009766, \quad P(10) = 0.000977
\]
Summing these values:
\[
P(8 \text{ or more}) = 0.043945 + 0.009766 + 0.000977 = 0.054688
\]
So, the probability of 8 or more girls is **0.054688**.

---

### c) Which of the above probabilities is relevant for determining if 8 girls in 10 births is significantly high (a or b)?
To determine if 8 girls in 10 births is significantly high, we are concerned with the probability of getting 8 or more girls (i.e., an extreme value). Therefore, **the probability calculated in part b** (0.054688) is more relevant because it considers 8 or more girls.

---

### d) Is 8 a significantly high number of births? Explain.
To determine whether 8 girls in 10 births is significantly high, we typically compare the probability of such an event (or more extreme events) to a threshold (e.g., 5%). The probability of 8 or more girls is 0.054688, which is slightly above 5%. Since it's not below 5%, 8 girls in 10 births is not usually considered "significantly high," though it is quite rare.

### Summary:
- a) Probability of exactly 8 girls: **0.043945**.
- b) Probability of 8 or more girls: **0.054688**.
- c) The probability in part **b** is relevant for determining significance.
- d) 8 girls in 10 births is **not significantly high** based on a typical 5% significance level.

---

Would you like more details or clarifications? Here are five related questions:

1. What is the probability of getting fewer than 3 girls in 10 births?
2. What is the probability of getting between 4 and 6 girls in 10 births?
3. How would the interpretation change if we considered a 1% significance level instead of 5%?
4. What assumptions are we making about the distribution of girls and boys in these births?
5. Can we use this data to estimate whether the gender distribution in births is biased?

**Tip:** When analyzing probabilities, always check if the event in question includes more extreme outcomes, especially when considering significance!

Consider the probability distribution for the number of girls in 10 births given below and answer the questions: a) What is the probability of exactly 8 girls in 10 births? b) What is the probability of 8 or more girls in 10 births? c) Which of the above probabilities is relevant for determining if 8 girls in 10 births is significantly high (a or b)? d) Is 8 a significantly high number of births? Explain.

Explore how to calculate the probability of getting 8 or more girls in 10 births using a probability distribution table. Learn about the significance of such results based on common statistical thresholds like 5%.

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