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Bab 5 Distribusi Normal © 2002 Prentice-Hall, Inc. Chap 5-1 Topik distribusi normal distribusi normal standar © 2002 Prentice-Hall, Inc. Chap 5-2 Distribusi Probabilitas Kontinu variabel random kontinu distribution probabilitas kontinu Values from interval of numbers Absence of gaps Distribution of continuous random variable Most important continuous probability distribution distribusi normal © 2002 Prentice-Hall, Inc. Chap 5-3 Distribusi Normal “Bell shaped” Symmetrical Mean, median and mode are equal Interquartile range equals 1.33 s Random variable has infinite range © 2002 Prentice-Hall, Inc. f(X) X Mean Median Mode Chap 5-4 Model Matematika f X 1 e 1 2s 2 X 2s 2 f X : density of random variable X 3.14159; e 2.71828 : population mean s : population standard deviation X : value of random variable X © 2002 Prentice-Hall, Inc. Chap 5-5 Beberapa Distribusi Normal distribusi normal dengan parameters © 2002 Prentice-Hall, Inc. s and , berbeda Chap 5-6 Menentukan Nilai Probabilitas Probability is the area under the curve! P c X d ? f(X) c © 2002 Prentice-Hall, Inc. d X Chap 5-7 Tabel yang digunakan? An infinite number of normal distributions means an infinite number of tables to look up! © 2002 Prentice-Hall, Inc. Chap 5-8 Distribution Normal Standar Cumulative Standardized Normal Distribution Table (Portion) Z .00 .01 Z 0 sZ 1 .02 .5478 0.0 .5000 .5040 .5080 Shaded Area Exaggerated 0.1 .5398 .5438 .5478 0.2 .5793 .5832 .5871 Probabilities 0.3 .6179 .6217 .6255 © 2002 Prentice-Hall, Inc. 0 Z = 0.12 Only One Table is Needed Chap 5-9 Contoh Z X s 6.2 5 0.12 10 Standardized Normal Distribution Normal Distribution s 10 5 © 2002 Prentice-Hall, Inc. sZ 1 6.2 X Shaded Area Exaggerated Z 0 0.12 Z Chap 5-10 Contoh P 2.9 X 7.1 .1664 Z X s 2.9 5 .21 10 Z X s 7.1 5 .21 10 Standardized Normal Distribution Normal Distribution s 10 .0832 sZ 1 .0832 2.9 5 © 2002 Prentice-Hall, Inc. 7.1 X 0.21 Shaded Area Exaggerated Z 0 0.21 Z Chap 5-11 Contoh: P 2.9 X 7.1 .1664(continued) Cumulative Standardized Normal Distribution Table (Portion) Z .00 .01 Z 0 sZ 1 .02 .5832 0.0 .5000 .5040 .5080 Shaded Area Exaggerated 0.1 .5398 .5438 .5478 0.2 .5793 .5832 .5871 0.3 .6179 .6217 .6255 © 2002 Prentice-Hall, Inc. 0 Z = 0.21 Chap 5-12 Contoh: P 2.9 X 7.1 .1664(continued) Cumulative Standardized Normal Distribution Table (Portion) Z .00 .01 .02 Z 0 sZ 1 .4168 -03 .3821 .3783 .3745 Shaded Area Exaggerated -02 .4207 .4168 .4129 -0.1 .4602 .4562 .4522 0.0 .5000 .4960 .4920 © 2002 Prentice-Hall, Inc. 0 Z = -0.21 Chap 5-13 Contoh: P X 8 .3821 Z X s 85 .30 10 Standardized Normal Distribution Normal Distribution s 10 sZ 1 .3821 5 © 2002 Prentice-Hall, Inc. 8 X Shaded Area Exaggerated Z 0 0.30 Z Chap 5-14 Contoh: P X 8 .3821 Cumulative Standardized Normal Distribution Table (Portion) Z .00 .01 Z 0 (continued) sZ 1 .02 .6179 0.0 .5000 .5040 .5080 Shaded Area Exaggerated 0.1 .5398 .5438 .5478 0.2 .5793 .5832 .5871 0.3 .6179 .6217 .6255 © 2002 Prentice-Hall, Inc. 0 Z = 0.30 Chap 5-15 Mengetahui nilai Z pada Probabilitas tertentu What is Z Given Probability = 0.1217 ? Z 0 sZ 1 Cumulative Standardized Normal Distribution Table (Portion) Z .00 .01 0.2 0.0 .5000 .5040 .5080 .6217 0.1 .5398 .5438 .5478 0.2 .5793 .5832 .5871 Shaded Area Exaggerated © 2002 Prentice-Hall, Inc. 0 Z .31 0.3 .6179 .6217 .6255 Chap 5-16 Nilai X untuk mengetahui Probabilitas Standardized Normal Distribution Normal Distribution s 10 sZ 1 .1179 .3821 5 ? X Z 0 0.30 Z X Zs 5 .3010 8 © 2002 Prentice-Hall, Inc. Chap 5-17 Assessing Normality (continued) Normal Probability Plot for Normal Distribution 90 X 60 Z 30 -2 -1 0 1 2 © 2002 Prentice-Hall, Inc. Look for Straight Line! Chap 5-18 Normal Probability Plot Left-Skewed Right-Skewed 90 90 X 60 X 60 Z 30 -2 -1 0 1 2 -2 -1 0 1 2 Rectangular U-Shaped 90 90 X 60 X 60 Z 30 -2 -1 0 1 2 © 2002 Prentice-Hall, Inc. Z 30 Z 30 -2 -1 0 1 2 Chap 5-19 Larger sample size P(X) Smaller sample size © 2002 Prentice-Hall, Inc. X Chap 5-20 Populasi Normal Population Distribution Central Tendency X Variation sX s n Sampling with Replacement © 2002 Prentice-Hall, Inc. s 10 50 Sampling Distributions n4 n 16 sX 5 s X 2.5 X 50 X Chap 5-21 Populasi tidak Normal Population Distribution Central Tendency X Variation sX s n Sampling with Replacement © 2002 Prentice-Hall, Inc. s 10 50 Sampling Distributions n4 n 30 sX 5 s X 1.8 X 50 X Chap 5-22 Central Limit Theorem As sample size gets large enough… the sampling distribution becomes almost normal regardless of shape of population X © 2002 Prentice-Hall, Inc. Chap 5-23 Contoh: 8 s =2 n 25 P 7.8 X 8.2 ? 7.8 8 X X 8.2 8 P 7.8 X 8.2 P sX 2 / 25 2 / 25 P .5 Z .5 .3830 Standardized Normal Distribution Sampling Distribution 2 sX .4 25 sZ 1 .1915 7.8 © 2002 Prentice-Hall, Inc. 8.2 X 8 X 0.5 Z 0 0.5 Z Chap 5-24