SOLUTION: A survey showed that 71% of adults need some form of vision correction (eyeglasses, contacts, surgery, etc.). Suppose 9 adults are randomly selected, and 8 of them turn out to need

Question 1192122: A survey showed that 71% of adults need some form of vision correction (eyeglasses, contacts, surgery, etc.). Suppose 9 adults are randomly selected, and 8 of them turn out to need some form of vision correction. Is 8 a significantly high number of adults who need vision correction out of 9 randomly selected adults?
Answer by CPhill(1959) (Show Source): You can put this solution on YOUR website!
Here's how to determine if 8 out of 9 adults needing vision correction is significantly high:
1. **Define "Significantly High":** We need to establish a threshold for what we consider "significantly high." A common approach is to use the range rule of thumb, which considers values outside of two standard deviations from the mean as significantly different.
2. **Calculate the Mean (μ):**
μ = n * p = 9 * 0.71 = 6.39
3. **Calculate the Standard Deviation (σ):**
σ = sqrt(n * p * (1-p)) = sqrt(9 * 0.71 * 0.29) ≈ 1.36
4. **Calculate the Range of Usual Values:**
* Lower Bound: μ - 2σ = 6.39 - 2 * 1.36 ≈ 3.67
* Upper Bound: μ + 2σ = 6.39 + 2 * 1.36 ≈ 9.11
5. **Compare the Observed Value:**
The observed value is 8.
6. **Make a Decision:**
Since 8 falls within the range of usual values (3.67 to 9.11), it is *not* considered significantly high.
**Conclusion:**
8 adults needing vision correction out of 9 randomly selected adults is within the expected range based on the given probability. Therefore, it is not considered a significantly high number.

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