# Viewer’s Guide to Against All Odds Part 18, The Sample Mean and Control Charts

Copyright © 2003–2024 by Stan Brown, BrownMath.com

Copyright © 2003–2024 by Stan Brown, BrownMath.com

x | P(x) |
---|---|

Roulette has 38 slots: 18 black, 18 red, 2 green.
P(Red) = ____/ ____ = __________.
x = amount won or lost on $1 bet.

μ = $ __________ = ________ cents,
σ = $ ________ = ________ cents.

Take a sample of n bets. Symbol for average won or lost
per bet in the sample is
_______.
This is the sample mean.
Many groups of n bets make a **distribution of sample means**.
The Central Limit Theorem tells you that’s almost a ____________
________________________.

The standard deviation of sample means has symbol ________ and equals σ / _______. The bigger the sample, the ______________ the variation in sample means.

For 50 $1 bets, σ_{x̅} =
________/√ ____= ____ cents.
Nearly every sample of 50 bets results in average outcome
of −47 cents to +37 cents per $1 bet.

For n = 1000 bets, μ still = __________ but
σ_{x̅} = ______.

For n = 100,000 bets, σ_{x̅} =
______ cent. That’s how the casino knows it can’t lose even
though some players may win.

**Central Limit Theorem Summary:**

1. The distribution of sample means is roughly ____________ when n
is __________
(gets closer for larger samples).

2. Mean of sample means: _______ = ___________.

3. S.D. of sample means: _______ = _________/_________.

**SPC Application: Control Charts**

Every ____ minutes, collect n = __ batches of Ruffles and
measure salt content.
Enter average on control chart, which plots ________________________
vertically and time horizontally. Control limits are
________ above and below target.

Frito Lay decision rules (other rules are possible):

(a) __ point(s) out of control (> 3 SD)

(b) __ out of __ points 2–3 SD on same side

(c) __ out of __ points 1–2 SD on same side

(d) A run of __ points on same side of mean

**The Giant of SPC: Dr.** __________________________________

He led __________ in rebuilding its economy after WW2; much later,
US companies began using his techniques. Memorable sayings:

(My favorite: “Do you know that? On what basis do you know that? Why do you take the 50% and do anything? Why don’t you put it in the wastebasket, where it belongs?”)

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