Question: 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 sample mean response of the 269 students was \(\bar{X}=137\) minutes. Assume that we know that the study time follows a normal distribution with standard deviation \(\sigma =65\) in the population of all first-year students at this university.

1. Use the survey result to give a 99% CI for the mean study time of all first-year students.
2. What condition not yet mentioned is needed for your confidence interval to be valid?

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