BrownMath.com → Statistics → AAO pt 18 Guide
Updated 30 June 2005

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

xP(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 =  ________/√ ____=  ____ 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 =  ______.
For n = 100,000 bets, σ =  ______ 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?”)