Question 1192121
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.