Using the Central Limit Theorem · Exercise 26

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

• 8.625
• 30.25
• 27.625
• 46.75
• 32.875
• 18.25
• 5
• 0.125
• 2.9375
• 6.875
• 28.25
• 24.25
• 21
• 1.5
• 30.25
• 71
• 43.5
• 49.25
• 2.5625
• 31
• 16.5
• 9.5
• 18.5
• 18
• 9
• 10.5
• 16.625
• 1.25
• 18
• 12.87
• 7
• 12.875
• 2.875
• 60.25
• 29.25

(a) In words, Χ = ______________
(b) (a) $\bar{x}$ = _____
(b) s_x = _____
(c) n = _____
(c) Construct a histogram of the distribution of the averages. Start at x = –0.0005. Use bar widths of ten.
(d) In words, describe the distribution of stock prices.
(e) 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.
(f) Use the ten averages from part e to calculate the following.
(a) $\bar{x}$ = _____
(b) s_x = _____
(g) Construct a histogram of the distribution of the averages. Start at x = -0.0005. Use bar widths of ten.
(h) Does this histogram look like the graph in part c?
(i) In one or two complete sentences, explain why the graphs either look the same or look different?
(j) Based upon the theory of the central limit theorem, $\bar{X}$ ~ _____(_____,____)

This is an open-ended exercise: its source gives no single answer.

OpenStax, Introductory Statistics 2e · §7.3 Using the Central Limit Theorem · Exercise 26