Warm-up
2.5 The Normal Distribution
Find the missing midpoint values, then find mean, median and standard deviation.
Student of the day!
Block 1
Student of the day!
Block 2
Student of the day!
Block 3
Student of the day!
Block 4
H.W. Discussion on E #56 and 57
Questions about 2.5 Reading
Bingo Review 2.1 to 2.4 (Slide 2)
3) Sometimes, Always or Never True:
The total area under a density curve (distribution curve)
And above the horizontal axis is 1.
4) The following table gives the results of an experiment in
which the ages of 525 pennies from current change were
recorded. "0" represents the current year, "1" represents
pennies one year old, etc.
Describe the shape of the data.
Bingo Review 2.1 to 2.4 (Slide 3)
5) The mean of a set of 150 values is 35, its median is 33, its
standard deviation is 6, and its IQR is 12. A new set is created
by first subtracting 10 from every term and then multiplying
by 5.
What other summary statistic, other than the standard
deviation, is 5 times greater in the new data set?
6)
 ( x  x)
i
n 1
2
Bingo Review 2.1 to 2.4 (Slide 4)
7) Sometimes, Always or Never True
If you added 25 to every value in the dataset, the
standard deviation will change.
8) What would be the shape of a histogram
displaying the results of 1000 repetitions of the # of
heads when flipping four coins at once ?
Bingo Review 2.1 to 2.4 (Slide 5)
9.
Bingo Review 2.1 to 2.4 (Slide 6)
10) In a normal distribution curve mean, _____, and
mode are all represented by the same number.
11) Histograms are best for displaying what kind of
numerical data?
Bingo Review 2.1 to 2.4 (Slide 7)
12. A distribution of SAT Math scores for 130 students at a
suburban high school provided the following statistics: Min.:
485, Q1: 502, Median: 520, Q3: 544, Max.: 610, Mean: 535,
Std. Dev.: 88. Which of the following is true?
A. The distribution is skewed to the left and there are no outliers.
B. The distribution is skewed left and there is at lease one
outlier.
C. The distribution is skewed to the right and there are outliers.
D. The distribution is skewed to the right and 65 students scored
better than 520.
E. The distribution is skewed to the right and 65 students scored
better than 535.
2.5 Normal Distribution
Where do you see it? Standardized test results,
probability, certain data collection from a large population.
More on Bell Curve
Standard Normal Distribution Curve
Z-Score =
x x
Sx
Practice Reading the Bell Curve using 68-95-99.7% Rule
1) What % of the data is below +1 ?
2) What % of the data is located between the
-2  and -1 ?
3) What percentile rank is at +1 ?
Checking for understanding using the standard normal
distribution curve and normal distribution curve
Using Normalcdf instead of 68-95-99.7% Rule
Leaving out mean and s.d.
Using calculator, entering z-score
a.
Using calculator, entering z-score
d.
Using calculator, entering values
a.
Using calculator, entering values
d.
Solving Problems with Normal Distribution
For Normal Distribution Problem, always draw the bell curve and
label the values of mean and standard deviations.
InvNorm
When given a % ile rank and you need to find a particular number of the
curve use Invnorm.
2nd Vars 3:InvNorm
InvNorm(% ile, Mean, St. Dev) InvNomr (%) will work for finding S.D. for
standard normal curve
OR InvNorm (%) for Standard normal dist. Curve to get a particular St.
Dev.
Example of its use
How many standard deviations above the mean is the 75% ile.
Back to N~(17,3) commuting problem.
How long does it take students to commute for those in the top 10% of
the distribution curve?
Next block
• Bring completed
Worksheet
• Draw a new normal
distribution curve for each
problem.
• Bring your textbook for the
review out of the textbook.
• Bring your notes organized
for the notebook check.
Ch. 1 and 2 Notebook Check
• 1.0 Types of Data and Graphs +
• 1.1 Data Exploration
• 1.2 Intro. to Summary Statistics
• 2.1 Visualizing Distributions
• 2.2 Graph Displays of Dist.
• 2.3 Measures of Center
• 2.4 Summary Statistics
• Warm-up sheet
• 2.5 Normal Distribution
Notes with warm-up 11 pts =77pts
(8pts notes, 3 pts warm-up = 11)
Ch. 2 Definitions ( 20pts)
+ means warm-up was on a
separate sheet
H.W. Answers to #56 and 57
#56 – Creating a cumulative % frequency plot.