Next section: Mean, σ estimated

Therefore, 468.02 ≤ μ ≤ 591.98. Naturally, if a larger sample size had been used, the range of scores would have been smaller.

The computation of the 99% confidence interval is exactly the same except that 2.58 rather than 1.96 is used for z. The 99% confidence interval is: 448.54 ≤ μ ≤ 611.46. As it must be, the 99% confidence interval is even wider than the 95% confidence interval.

- Compute M = ΣX/N.
- Compute
- Find z (1.96 for 95% interval; 2.58 for 99% interval)
- Lower limit = M - z σ
_{M} - Upper limit = M + z σ
_{M} - Lower limit ≤ μ ≤ Upper
limit

- Normal distribution
- σ is known
- Scores are sampled randomly and are independent

Next section: Mean, σ estimated