Question: Student study times. A class survey in a large class for first year college students asked, "About how many minutes do you study on a typical weeknight? The mean response of the 269 students was \(\bar{x}=137\) minutes. Suppose that we know that the study time follows a Normal distribution with standard deviation \(\sigma=65\) minutes in the population of all first-year students at this university.

1. Use the survey result to give a \(99 \%\) confidence interval for the mean study time of all first-year students.
2. What condition nor yet mentioned is needed for your confidence interval co be valid?

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