problem 1: Your factory has a machine for drilling holes in a sheet metal part. The mean diameter of the hole is 10mm with a standard deviation of 0.1mm. What is the probability that any single hole will have diameter between 9.9mm and 10.1mm?
If you perform quality testing on samples of 100 parts coming off of this machine, what do you expect the mean, standard deviation, and shape of the distribution of the average diameter of holes in the quality samples to be? Why is it true that you can make these assumptions?
What is the chance that a set of 64 holes will have an average diameter between 9.99mm and 10.01mm?
problem 2: According to a Gallup poll 51% of US women prefer to have a job outside of the home.
What is the chance that a survey of 200 women would find that 45% or less of the respondants would prefer a job outside of the home?
Your mother sees a survey of 10 women with 4 stating they would prefer a job outside of the home? (In particular, is this an indication that women really prefer to stay at home?)
What would you recommend to give your mother a better sense of the women’s feelings about jobs?
problem 3: The same survey showed 37% of Republican voters women would prefer a job outside of the home.
What is the standard deviation of this poll for a survey of 400 Republican women?
What is the likelihood that you would survey this group and find 59% or more of Republican women would agree with this statement?