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Part 1

The accompanying table describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children. Complete parts​ (a) through​ (d) below.

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Part 1

**a.** Find the probability of getting exactly 6 girls in 8 births.

enter your response here**** 

​(Type an integer or a decimal. Do not​ round.) 

Number of

Girls x

​P(x)

0

0.001

1

0.039

2

0.117

3

0.197

4

0.292

5

0.197

6

0.117

7

0.039

8

0.001

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The table provides the **probability distribution** for the number of girls (\(x\)) out of 8 children, with each value of \(P(x)\) corresponding to the probability of getting exactly \(x\) girls.

### Part (a): Find the probability of getting exactly 6 girls in 8 births.

From the provided table:
- \(x = 6\)
- \(P(6) = 0.117\)

Thus, the probability of getting exactly 6 girls in 8 births is:  
\[
P(6) = 0.117
\]

So, the answer is:

**0.117**

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Would you like me to walk through how these probabilities are calculated (using binomial distribution formulas)? Or do you have other questions related to this problem?

Here are 5 related questions:
1. What is the probability of getting at least 5 girls in 8 births?
2. What is the probability of getting no more than 4 girls?
3. How do you calculate the mean and standard deviation of a binomial distribution?
4. If the probability of a girl birth is 0.5, how would the probabilities change for each \(x\)?
5. How can cumulative probabilities be useful in interpreting this table?

**Tip:** In a binomial distribution, the sum of all individual probabilities \(P(x)\) should always equal 1.

The accompanying table describes results from groups of 8 births from 8 different sets of parents. The random variable x represents the number of girls among 8 children. Complete parts​ (a) through​ (d) below. a. Find the probability of getting exactly 6 girls in 8 births.

This problem explores the probability of getting exactly 6 girls in 8 births using a binomial distribution. Learn how to apply the binomial probability formula to calculate the probability, with key concepts in probability and statistics. Suitable for students in Grades 10-12.

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