2. Stats Bar n Grill
Tonight’s Menu
Organizing Data- Rocco
Basic Probability-Frida
Probability & Binomial Distributions-John
Regression & Correlation-Frankie
3. I. Lesson 2
Class Frequency Relative Cumulative Class Boundaries
(f) Frequency Frequency Mark
menu prices f/n midpoint
$2.75-$4.95 25 0.125 25 $3.85 $2.745-$4.955
$4.96-$7.15 50 0.25 75 $6.05 $4.955-$7.155
$7.16-$9.35 38 0.19 113 $8.25 $7.155-$9.355
$9.36.$11.55 45 0.225 158 $10.45 $9.355-$11.555
$11.56-$13.75 10 0.05 168 $12.65 $11.555-$13.755
$13.76-$15.95 15 0.075 183 $14.85 $13.755-$15.955
$15.96-$18.15 12 0.06 195 $17.05 $15.955-$18.155
$18.16-$18.95 5 0.025 200 $18.55 $18.155-18.955
n=200 1
4. II. Lessons 8,9,10,11
Valet Parking experiment
Experimental (Imperial) Probability
Outcome 0≤P(Event)≥1
Study for November: n=312 cars
event= 22 accidents
P(accident)= 22÷312= 0.07=7%
P(accident)’=290÷312= 0.93=93%
5. II. Lessons 8,9,10,11
How can our restaurant use these statistics?
Insurance rates
Keep track of how the probability is changing
Advertise the valet parking
Different use of statistics and why you always should think
twice:
93% non-accident rate sounds great
7% chance that your car is involved in an accident does
sound worse
Have to question how big was the sample size, over what
period of time etc. To determine the credibility.
6. II. Lessons 8,9,10,11
Looking at the 22 cars involved in accidents over the month and how
they were spread through the week days in a CONTINGENCY TABLE:
Day Scratch Dent Marginal Total
Monday 0 0 0
Tuesday 1 0 1
Wednesday 2 1 3
Thursday 3 2 5
Friday 4 3 7
Saturday 3 2 5
Sunday 1 0 1
Marginal Total 14 8 22
7. II. Lessons 8,9,10,11
Addition Rule:
P(AorB)=P(A)+P(B)-P(A∩B)
P(Scratch)= (14÷22)= 0.64=64%
P (Dent)= (8÷22)= 0.36= 36%
P(Scratch or Dent)= (14÷22)+(8÷22)=22÷22= 1=100%
Mutually exclusive
P(Friday or Dent)= (7÷22)+(8÷22)-(3÷22)= 12÷22=0.55=55%
P(Wednesday or Scratch)= (3÷22)+(14÷22)-(2÷22)= 15÷22=0.68=68%
Not mutually exclusive
8. II. Lessons 8,9,10,11
Conditional probability-given information
P(Dent|Saturday)= (2|5)= 2÷5=0.4=40%
P(Sunday|Scratch)= (1|1)= 1÷1=1=100%
Multiplication Rule-more than one selection
• Choose 2 days
P(Fri. and Sat.)=(7÷22)×(5÷22)= 12÷22=0.55=55%
P(Mon and Tue)= Day Scratch Dent Marginal Total
(0÷22)×(1÷22)= Monday 0 0 0
1÷22=0.045=4.5% Tuesday 1 0 1
Wednesday 2 1 3
Thursday 3 2 5
Friday 4 3 7
Saturday 3 2 5
Sunday 1 0 1
Marginal Total 14 8 22
9. II. Lessons 8,9,10,11
How can the restaurant use the weekly table
and the probability generated from that?
Insurance purposes
Legal purposes
Manager evaluations
Space
Staffing
10. III. Lesson 19
Applications of the Normal Distribution
μ 23.58
σ 3.68
What is the probability that
a patron to Stat’s Bar & Grill
will spend an amount
between $25.00 and $33.00
on a meal?
11. III. Lesson 19
Cont. Applications of the Normal Distribution
Let x be the random variable which represents
how much a patron spends on his meal:
P(25<x<33)
Remember the z score formula:
Z=X-μ
σ
12. III. Lesson 19
Cont. Applications of the Normal Distribution
Z score for $25.00 Z score for $33.00
(25-23.58)/3.68=0.39 (33-23.58)/3.68=2.56
Z Table= .1517 Z Table Value=
.4948
13. III. Lesson 19
Cont. Applications of the Normal Distribution
.4948- .1517=.3431
There is a 34.31% probability that a patron will
spend an amount between $25.00 and $33.00
on a meal at Stats Bar & Grill.
14. IV. Lessons 30, 31
Correlation and Regression
Determine the amount of staff needed daily.
Discover minimum staffing needs for special
functions.
Does the amount of customers influence the
staffing needs?
Is it a Positive or Negative correlation?
