Preview - Sampling Distributions 2021

Central Limit Theorem applications

Dr. Lopez gives students 90 minutes to complete the final exam for her course. Most students use almost all the time allowed, and relatively few students finish early, so the distribution of times that it takes students to finish the exam is strongly skewed to the left. The mean and standard deviation of the finishing times are 85 and 10 minutes, respectively. 

Suppose we took random samples of 40 students and calculated \(\bar x\) as the sample mean finishing time. We can assume that the students in each sample are independent.

Questions

Please answer the questions below.

What would be the shape of the sampling distribution of \(\bar x\)?

Without doing any calculations, which of the following has a HIGHER probability:

  • 1 randomly selected student taking more than 90 minutes to complete the final exam (meaning that they did not turn in the exam before the 90 minutes expired)
  • 30 randomly selected students having a sample mean greater than 90 minutes

Justify your reasoning using appropriate statistical language. 

Explain why you cannot use a Normal distribution to calculate the probability of the first event in Question 5.2

Notes

These notes will appear on every page in this lesson so feel free to put anything here you'd like to keep track of.