A statistics professor would like to set the difficulty for an exam

such that 90% of the 170 students writing complete it in less than 2.5 hours. To estimate the difficulty ahead of delivery, 4 proxies completed the exam beforehand with a mean time of 2.2 hours and a standard error of 0.3 hours. A probability table for a normal (z) distribution appears at the end of this test paper.

Question 1
Is there a difference between 90% of students completing the exam in under 2.5 hours and being 90% confident that the mean completion time is under 2.5 hours? Explain.

Question 2
If the sample is taken to be representative of the population, would you expect 90% of students to complete the exam in under 2.5 hours?

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