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 57Questions 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 inwhich the ages of 525 pennies from current change wererecorded. "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, itsstandard deviation is 6, and its IQR is 12. A new set is

createdby first subtracting 10 from every term and then multiplyingby 5.

What other summary statistic, other than the standard deviation, is 5 times greater in the new data set?

6) 1

)( 2

n

xxi

Bingo Review 2.1 to 2.4 (Slide 4)

7) Sometimes, Always or Never TrueIf you added 25 to every value in the dataset, thestandard 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 asuburban 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 DistributionWhere 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 = Sx

xx

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-scorea.

Using calculator, entering valuesa.

Using calculator, entering z-scored.

Using calculator, entering valuesd.

Solving Problems with Normal DistributionFor Normal Distribution Problem, always draw the bell curve and

label the values of mean and standard deviations.

InvNormWhen 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 useHow 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.