1. Unit 7 Sampling Distributions

10. SizeMean (yrs)Stdev (yrs) Population12.269.61 n = 412.314.80 n = 1612.242.32 n = 4912.291.30

11. https://en.wikipedia.org/wiki/Mathematics #Mathematics_as_science

17.  But most population distributions are not approximately normal.

22. Example 1: Soda cans are filled such that the volume is approx. normally dist. with a mean of 12 oz and a stdev of 0.15 oz. Suppose we select 16 cans and find an average volume of 11.83 oz. Is this unusual?

23. Example 2: Acme Fasteners Co. produces bolts which are supposed to have a mean diameter of 0.5 inches and a standard deviation of 0.02 inches.

24. Example 2, con’t: The machine will be shut down and recalibrated if the mean diameter of the bolts is less than 0.49 or greater than 0.51 inches.

25. Example 2, con’t: Suppose you take a sample of 37 bolts. What is the approx. probability that the machine will be shut down unnecessarily?

26. Example 3: Suppose that the weights of people are approx. normally distr. with mean 164 lbs and stdev 23 lbs. 16 people get on an elevator which states the following:

27. Example 3, con’t: “No more than 16 persons. Weight limit 2500 lbs.” What is the approx. prob. that the elevator will be over the limit?

28. Example 4: Mini-Mart receipts show that customer purchases have a skewed dist. with mean $32 and stdev $20.

29. Example 4, con’t: What is the prob. that one customer will make a purchase greater than $40?

30. Example 4, con’t: Is it likely that the next 50 customers will spend an average of at least $40?

31. Example 5: Pollution (CO emissions) for a specific make and model of a car vary with a mean of 2.9 g/mile and a stdev of 0.4 g/mile. Your company owns 8 of these cars. BVD p. 430

32. Example 5, con’t: Say your 8 cars get an average of 2.75 g/mile of CO emissions. Is this unusual? BVD p. 430