7.3 Exercise 39

The closing stock prices of 35 U.S. semiconductor manufacturers are given as follows.

1. 8.625
2. 30.25
3. 27.625
4. 46.75
5. 32.875
6. 18.25
7. 5
8. 0.125
9. 2.9375
10. 6.875
11. 28.25
12. 24.25
13. 21
14. 1.5
15. 30.25
16. 71
17. 43.5
18. 49.25
19. 2.5625
20. 31
21. 16.5
22. 9.5
23. 18.5
24. 18
25. 9
26. 10.5
27. 16.625
28. 1.25
29. 18
30. 12.87
31. 7
32. 12.875
33. 2.875
34. 60.25
35. 29.25

1. In words, Χ = ______________
2. 1. $\bar{x}$ = _____
   2. s_x = _____
   3. n = _____
3. Construct a histogram of the distribution of the averages. Start at x = –0.0005. Use bar widths of ten.
4. In words, describe the distribution of stock prices.
5. Randomly average five stock prices together. (Use a random number generator.) Continue averaging five pieces together until you have ten averages. List those ten averages.
6. Use the ten averages from part e to calculate the following.
   1. $\bar{x}$ = _____
   2. s_x = _____
7. Construct a histogram of the distribution of the averages. Start at x = -0.0005. Use bar widths of ten.
8. Does this histogram look like the graph in part c?
9. In one or two complete sentences, explain why the graphs either look the same or look different?
10. Based upon the theory of the central limit theorem, $\bar{X}$ ~ _____(_____,____)