For 100 births, P(exactly 57 girls) = 0.0301 and P(57 or more girls) = 0.097. Is 57 girls in 100 births a significantly high number of girls? Which probability is relevant to answering that question?
Consider a number of girls to be significantly high if the appropriate probability is 0.05 or less.
The relevant probability is
so 57 girls in 100 births
a significantly high number of girls because the relevant probability is
0.05.

To determine if 57 girls in 100 births is a significantly high number, we need to compare the relevant probability to the threshold of 0.05.

Here’s the process for determining this:

1. **P(exactly 57 girls)** = 0.0301: This is the probability of having exactly 57 girls. However, this probability doesn't tell us if the number of girls is significantly high, because it only covers one specific outcome (exactly 57).

2. **P(57 or more girls)** = 0.097: This is the cumulative probability of having 57 or more girls. This is the probability that encompasses 57, 58, 59, and so on. To determine if 57 girls is significantly high, we need to look at how unusual the outcome of 57 or more girls is, relative to the threshold of 0.05.

**Which probability is relevant?**
The relevant probability to consider for determining if 57 girls is a significantly high number is **P(57 or more girls)**, since we are looking at how extreme the outcome of 57 or more girls is.

**Is 57 girls a significantly high number?**
The probability of 57 or more girls is 0.097, which is greater than 0.05. Therefore, 57 girls is **not** considered a significantly high number of girls, because the probability exceeds the 0.05 threshold.

### Summary:
- The relevant probability is **P(57 or more girls)**.
- 57 girls in 100 births is **not** a significantly high number because the relevant probability is **0.097**, which is greater than **0.05**.

Would you like further details or clarifications on this explanation?

### Related questions:
1. How do we calculate cumulative probabilities in a binomial distribution?
2. What does "significantly high" or "significantly low" mean in terms of probability?
3. How can we use a normal approximation to estimate binomial probabilities?
4. What role does the mean and standard deviation play in determining significance in large trials?
5. How do we interpret P-values in hypothesis testing?

**Tip:** When dealing with cumulative probabilities, always compare them to your significance level (0.05 in this case) to determine if an outcome is unusual.

For 100 births, P(exactly 57 girls) = 0.0301 and P(57 or more girls) = 0.097. Is 57 girls in 100 births a significantly high number of girls? Which probability is relevant to answering that question? Consider a number of girls to be significantly high if the appropriate probability is 0.05 or less.

Determine if having 57 girls in 100 births is a significantly high number using binomial distribution. Explore concepts such as cumulative probability and significance testing. Learn how P(57 or more girls) = 0.097 indicates that 57 girls is not significantly high since the probability is greater than the 0.05 threshold.

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