Answer: The smallest sample size would be 392.
Explanation:
Since we have given that
Standard deviation = 12 minutes
Mean = 68 minutes
Margin of error = [tex]\pm 1[/tex]
At 90% confidence interval, z = 1.65
So, the smallest sample size that we should consider would be
[tex]n=(\dfrac{z\times \sigma}{ME})^2\\\\n=(\dfrac{1.65\times 12}{1})^2\\\\n=(19.8)^2\\\\n=392.04\\\\n=392[/tex]
Hence, the smallest sample size would be 392.
