Step-by-step explanation:
Margin of error = critical value × standard error
The standard error is:
s = σ / √n
s = 7.4 / √664
s = 0.287
The population is normally distributed, so the critical value can be found from a z-score table.
For 90% confidence, z = 1.645.
For 95% confidence, z = 1.960.
For 99% confidence, z = 2.576.
The margins of error are:
90%: 1.645 × 0.287 = 0.4724
95%: 1.960 × 0.287 = 0.5629
99%: 2.576 × 0.287 = 0.7398
The mean is 26.6, so the confidence intervals are:
90%: (26.6 − 0.47, 26.6 + 0.47) = (26.13, 27.07)
95%: (26.6 − 0.56, 26.6 + 0.56) = (26.04, 27.16)
99%: (26.6 − 0.74, 26.6 + 0.74) = (25.86, 27.34)
