SOLUTION: The table below describes results from random selection of eight live births from eight different sets of parents. The random variable x represents the number of girls among the ei
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Question 1192121: The table below describes results from random selection of eight live births from eight different sets of parents. The random variable x represents the number of girls among the eight live births. Is 6 a significantly high number of girls out of 8 live births?
Probability Distribution of Girls in x Live Births
x P(x)
0 0.004
1 0.008
2 0.104
3 0.251
4 0.266
5 0.251
6 0.104
7 0.008
8 0.004
You can put this solution on YOUR website! Here's how to determine if 6 girls out of 8 live births is significantly high:
1. **Calculate the Mean (μ):**
μ = Σ [x * P(x)]
μ = (0 * 0.004) + (1 * 0.008) + (2 * 0.104) + (3 * 0.251) + (4 * 0.266) + (5 * 0.251) + (6 * 0.104) + (7 * 0.008) + (8 * 0.004)
μ = 4
2. **Calculate the Standard Deviation (σ):**
σ = sqrt( Σ [(x - μ)² * P(x)] )
σ = sqrt( (0-4)² * 0.004 + (1-4)² * 0.008 + (2-4)² * 0.104 + (3-4)² * 0.251 + (4-4)² * 0.266 + (5-4)² * 0.251 + (6-4)² * 0.104 + (7-4)² * 0.008 + (8-4)² * 0.004 )
σ ≈ 1.27
3. **Calculate the Range of Usual Values (using the Range Rule of Thumb):**
* Lower Bound: μ - 2σ = 4 - 2 * 1.27 ≈ 1.46
* Upper Bound: μ + 2σ = 4 + 2 * 1.27 ≈ 6.54
4. **Compare the Observed Value:**
The observed value is 6 girls.
5. **Make a Decision:**
Since 6 falls within the range of usual values (1.46 to 6.54), it is *not* considered significantly high.
**Conclusion:**
6 girls out of 8 live births is within the expected range based on the given probability distribution. Therefore, it is not considered a significantly high number.
