Download File

Honors Stats Day 13
Quiz and Normal Dist
SILENT DO NOW
ON DESK:
Chapter 5 Practice Quiz
DO NOW:
Check HW with key and grading pen
Homework:
Ch 6 #17-19
Quiz Chapter 5
•
Making Boxplots
•
Reading Boxplots (SOCS and Interpret)
•
Mean vs Median
•
Standard Deviation
Boxplot Exit Ticket
NEVER INCLUDE Q2
• (Based on AP Test)
•
QUIZ +
Calculator Sheet
•
•
Pass in Quiz and Practice Calculator
Work with the following data set:
5, 6, 12, 12, 12, 15, 18, 20, 22, 56
Random Data
•
•
•
Remember:
Data that is completely random (no
bias) should present with a NORMAL
DISTRIBUTION among the
population
Ex. Heights of men, the “bell curve”
A Normal Distribution
Standard Deviation
MEAN
Drawing Normal
Models
•
Notation: N ( mean, standard dev )
•
Example: N(18,3)
Sketch the Normal
Distribution
1) N(500, 100)
• 2) N(100, 16)
•
Honors Stats Day 14
Review
SILENT DO NOW
ON DESK:
Chapter 6 #17a-19a
DO NOW:
ACT Do Now
Check HW with key and grading pen
Homework:
Chapter 6 #17-19, Chapter 6 Notes
A Normal Distribution
Standard Deviation
MEAN
Drawing Normal
Models
•
Notation: N ( mean, standard dev )
•
Example: N(18,3)
Sketch the Normal
Distribution
1) N(500, 100)
• 2) N(100, 16)
•
Knowing Extremes
Normal models show how LIKELY it is to find
a value that far from the mean
or what percentage of the data fell below,
above, or between given value(s)
Sketch and Describe
•
•
•
•
Sketch the distribution of the
birthweights of babies: N(7.6lb, 1.3lb)
We are 68% sure that the baby will be born between
______lb and ______lb.
We are 99.7% sure that the baby will be born
between _____lb and _____lb.
What is the likelihood that the baby will be less than
8.9 lbs?
You try
•
•
The distribution of body
temperatures is modeled normally as
N(98.2, 0.6). Describe the
distribution.
What is the probability that your
body temp is below 97 degrees?
Unusual
•
We say something is “unusual” if it is
more than 2 standard deviations
from the center/mean (from the
“norm”)
Worksheet and Board
Practice
Honors Stats Day 15
SILENT DO NOW
ON DESK:
Chapter 6 #17-19, notes
DO NOW:
Check HW with key and grading pen
68-95-99.7 Exit Slip
Homework:
Ch 6 #5-7, 9, 29, 30, 33, 34
Objective
•
SWBAT calculate probability using
the standard normal curve and zscore chart
Last Week…
We have 2 problems with this..
• 1) How do we use this model to find
probability that is not exactly ±1,
±2, or ±3, SDs away from the
mean?
•
•
2) Can we use this to compare two
completely different data sets??
Notice…
•
We have been talking in terms of
“Number of Standard Deviations
Away from the Mean”…
Another way to see
it…
•
•
Let’s look at it as number of
standard deviations away from
the center (the mean)…
And define it as the Z-SCORE!
The Normal
Distribution
Notice how each line
represents the
number of standard
deviations away
from the mean..or
the…
Z-SCORE!!!
Standard Deviation
MEAN
Z-score as a shift and
rescale of distribution
•
•
•
•
When we make a z score, we take each data
point and subtract a number (the mean)
What would happen to the graph y=x if we subtracted 1 from each x
value y=(x-1)?
What changes?? We shift everything over (mean becomes 0)
We subtract EVERY VALUE by that number
What does not change??
SPREAD: Standard Deviation, Range, IQR
Shift and Rescale
•
When we make a z score, we also take
each data point and divide by a number
(the standard deviation)
CHANGING OUR SCALE TO
STANDARD DEVIATION
The Standard Normal
Curve
•
The Distribution of Z-SCORES!
THERE ARE NO UNITS! It’s the
same for every set of data, no
matter what you are talking
about! YAY!
Comparisons
•
Compare earning a 21 on the ACT
N(20.8, 2.4) to earning a 1200 on
the SAT N(1020, 184). Which one
did the person do better on?
Comparisons
Who’s more respected in their
workplace based on pay:
• A teacher who is paid $70,000 when
the avg teacher pay at the school is
$45,000 with an SD of $9,000 or a
consultant who earns $92,000 when
the average is $80,000 with an SD of
$5,000.
•
Comparisons
•
Chapter 4 Quiz P2: Mean = 19.2
SD = 0.5
Maria got a 19
Chapter 4 Quiz P3: Mean = 19.2
SD = 1.8
Leslie got an 19
Who did better on the quiz
compared to their class?
Comparing 2
Different Data Sets
•
We need a way to compare 2
different data sets taking into
account BOTH the…
average
• standard deviation
•
If we make their averages the same (0),
we can use the SD as a way of
measuring… hence the Z-SCORE
One More: Which is
fatter?
•
•
•
Which is fatter, the cat or the dog?
The cat weighs 13lbs and cats on
average weigh 9lbs with a standard
deviation of 2.1 lbs.
The dog weighs 72 lbs when they on
average weigh 50 lbs with a standard
deviation of 15.8lbs.
If it’s not exactly ±1,
±2, or ±3 SDs from
the mean
•
•
Consdier the SAT again: N(1020, 184)
Suppose you earned a 1200 on the SAT.
What percentile are you?
(PERCENTILE=%THAT YOU BEAT!)
1. Find Z score
2. What percent is to the LEFT??
THE CHART ONLY GIVES YOU
WHAT IS ON THE LEFT!
•
•
N(1020,184)
Suppose you earned a 1200 on the SAT.
What percent of test takers did better than
you?
1. Find Z score
2. What percent is to the RIGHT??
(Draw a picture)
The percent the chart will give you is
the percent to the left…
To get the right, subtract from 100!
Z-SCORE CHART
1.
2.
3.
4.
Find your z-score
Draw a picture- vertical line at zscore and shade
Look up z-score to tell you percent to
the LEFT of your score (less than your
score) Note: this is the percentile
Determine if you want that percent
(less than) or 100-[that percent]
(more than)
Z-Score
•
1. What is the likelihood that you scored
below an 18 on this last ACT given
N(18.8, 3.7)?
•
2. That you scored above a 20?
•
3. That you scored above a 22.5?
•
4. What percentile are you if you scored a
24?
Honors Stats Day 16
SILENT DO NOW
ON DESK:
Chapter 6 #5-7, 29, 30, 33, 34
DO NOW:
Check HW with key and grading pen
Homework:
Quick Review
1) z < 2.88
• 2) z<-0.11
• 3) z > 0.24
• 4) -1.31 < z
• 5) Drink prices at a coffee shop are
distributed normally N(3.25, 1.00).
What is the probability that your
drink will cost more than $5?
•
Challenge
•
•
Life span is distributed normally
N(71, 14). What is the probability
that you will live to at least 75 but no
older than 90?
Hint: Draw a Picture!
•
Find the percentages for each and
subtract the larger from the
smaller!
Finding the Between
•
Find the percentages for each and
subtract the larger from the smaller!
Practice again!
•
What is the chance that a baby
weighs between 4.5 oz and 8.5 oz
given N(6, 1.7)?
Board Practice
Trashketball!
•
•
•
You can use your notes
Everyone in your group must have
an answer
To get the shots, everyone in group
raises hands with completed work
raised hand and not done?
Disqualified from round
•
After each problem, the winning
group will show work
Question 1
•
What percentile am I if I scored a 25
on the ACT that is normally
distributed with N(21, 3.2)?
Question 2
•
What is the chance that I scored
above a 93 on a test that was
normally distributed as follows:
N(88, 3.6)?
Question 3
•
What percent of basketball players
have less than a .6 shooting
percentage at the free-throw line if it
is normally distributed N(.71, .09)
Question 4
What percent of students score
between a 21 and a 26 on the ACT
that is normally distributed
• N(21, 3.2)?
•
Question 5
•
What percent of M&M packages
weigh between 2.4 and 2.6 ozs given
N(2.43, 0.4)?
Question 6
•
What percent chance is there that
you will score more than 2 goals in a
game given N(2.4, 0.8)
Question 7
•
Chip bag weights are normally
distributed with a mean of 1.8 oz
with a SD of .1oz. What is the
probability of getting a chip bag that
weighs 2 oz or more?
Question 8
•
Labrador retriever life spans are
normally distributed N(11.8, 1.3).
What is the probability that your
chocolate lab lives between 14 and
15 years?
Question 9
•
The average room temperature in
Pritzker is 70 degrees Fahrenheit
with an SD of 5 degrees. What is the
probability that your next room will
be between 68 and 72 degrees?
Question 10
•
Who is a better choice for the ad
campaign if Ronaldo attracts an
average of 1 million viewers with an
SD of .023 million while Lebron
James attracts an average of .9
million with an SD of .011 million?
Question 11
Which is a better deal: a $16000
yamaha motorcycle which averages
• $15000 with an SD of $1900, or
a$23000 Harley motorcycle which
averages $21000 with an SD of
$2400?
•
CHALLENGE
•
I got in the 95th percentile for the
SAT N(1020,184). What was my
score on the SAT?
Finding scores from
percents
•
Say a school only accepts students in
the top 10%(90th percentile). If the
ACT is normally distributed N(21,
3.2), what score would you need to
get on your ACT?
WORK BACKWARDS
1. Draw a picture
2. Determine percent to the left
3. Find z in chart from percent
4. Plug in equation and solve for x
Another Example
•
The organic chemistry class at
Boston College, after their first test,
suggests to its lowest 15% of
students that they should drop the
course. If the class has a distribution
of N(78, 8.2), what score would you
have to be above to stay in the
class?
Another Example
•
My friend just had a premature baby
that was born in the 30th percentile
of baby weights. If newborns have a
normally distributed weight modeled
by N(7.5lbs, 1.25lbs), how much did
my friend’s baby weigh?
Exit Ticket