Binomial Fixed number trials Independent trials Only two outcomes p is constant Calculator: binompdf(n,p,x) (for equal to) binomcdf(n,p,x) (for less than or equal to)

Normal Bell-shaped curve Center is mean Standard deviation controls “spread” 68, 95, 99.7 Calculator: normalcdf(a,b,mean, stdev) (for between a and b) invNorm(p, mean, stdev) (for area to the left equal to p)

Comparing Normal to Binomial Differences Similarities

Approximating Binomial with Normal Decide whether this is a good idea: Figure out which normal curve to use: Don’t forget the continuity correction:

Exercise P 227 Data and Probability Connections: Mathematics for Middle School Teachers, Perkowski and Perkowski. Pearson Prentice Hall, NJ, 2007.

Sampling Distributions Find a random sample Statistic: a number that describes the sample. Statistics are random, too. Mean Standard Deviation

Population 1 104.5 16 104.3 31 73.8 46 129.6 61 92.8 2 124.1 17 90.4 32 110.7 47 125.6 62 139.1 3 86.7 18 81.7 33 129.0 48 93.8 63 57.8 4 69.7 19 82.4 34 157.7 49 112.3 64 119.4 5 103.0 20 120.1 35 114.7 50 137.2 65 100.9 6 128.9 21 84.4 36 110.0 51 97.7 66 73.6 7 122.3 22 91.6 37 97.4 52 85.7 67 93.5 8 100.6 23 132.0 38 103.5 53 107.8 68 96.1 9 71.1 24 85.6 39 101.2 54 72.0 69 80.5 10 77.0 25 117.3 40 122.7 55 99.3 70 137.1 11 138.5 26 94.8 41 105.4 56 72.6 71 136.9 12 78.7 27 101.0 42 82.5 57 83.9 72 86.2 13 112.1 28 87.5 43 140.4 58 103.2 73 92.0 14 122.9 29 108.4 44 108.8 59 149.1 74 86.9 15 87.2 30 81.6 45 60 153.5 75 104.8

Histogram of Population

Central Limit Theorem http://kitchen.stat.vt.edu/~sundar/java/applets/CLTApplet.html http://bcs.whfreeman.com/pbs/cat_050/pbs/CLT-Binomial.html

Homework Data and Probability Connections p 233 number 20. Data and Probability Connections p 262 numbers 5, 9, and 10.