**The standard IQ test has a mean of 96 and a standard deviation of 14. We want to be 99% certain that we are within 4 IQ points of the true mean. Determine the required sample size.**

**Answer:**

Confidence Level = 99% -> α=2.576

σ = 14

Confidence Interval = 96 ± 4 = (92, 100)

-> 96-92 = 100-96 = 4

x̅ = 96

Confidence Interval = x̅ ± z_α/2 * (σ/√n)

4 = z_α/2 * (σ/√n)

4 = 2.576 * (14/√n)

n = 81.28 ≈ 81