Bab 5 Distribusi Normal © 2002 Prentice-Hall, Inc.

Topik distribusi normal distribusi normal standar © 2002 Prentice-Hall, Inc.

Distribusi Probabilitas Kontinu variabel random kontinu Values from interval of numbers Absence of gaps distribution probabilitas kontinu Distribution of continuous random variable Most important continuous probability distribution distribusi normal © 2002 Prentice-Hall, Inc.

Distribusi Normal “Bell shaped” Symmetrical Mean, median and mode are equal Interquartile range equals 1.33 s Random variable has infinite range f(X) X  Mean Median Mode © 2002 Prentice-Hall, Inc.

Model Matematika © 2002 Prentice-Hall, Inc.

Beberapa Distribusi Normal distribusi normal dengan parameters  and , berbeda © 2002 Prentice-Hall, Inc.

Menentukan Nilai Probabilitas Probability is the area under the curve! f(X) X c d © 2002 Prentice-Hall, Inc.

Tabel yang digunakan? An infinite number of normal distributions means an infinite number of tables to look up! © 2002 Prentice-Hall, Inc.

Distribution Normal Standar Cumulative Standardized Normal Distribution Table (Portion) .02 Z .00 .01 .5478 0.0 .5000 .5040 .5080 Shaded Area Exaggerated 0.1 .5398 .5438 .5478 0.2 .5793 .5832 .5871 Probabilities Z = 0.12 0.3 .6179 .6217 .6255 Only One Table is Needed © 2002 Prentice-Hall, Inc.

Contoh Standardized Normal Distribution Normal Distribution Shaded Area Exaggerated © 2002 Prentice-Hall, Inc.

Standardized Normal Distribution Contoh Standardized Normal Distribution Normal Distribution Shaded Area Exaggerated © 2002 Prentice-Hall, Inc.

Contoh: (continued) Cumulative Standardized Normal Distribution Table (Portion) Z .00 .01 .02 .5832 0.0 .5000 .5040 .5080 Shaded Area Exaggerated 0.1 .5398 .5438 .5478 0.2 .5793 .5832 .5871 Z = 0.21 0.3 .6179 .6217 .6255 © 2002 Prentice-Hall, Inc.

Contoh: (continued) Cumulative Standardized Normal Distribution Table (Portion) Z .00 .01 .02 .4168 -03 .3821 .3783 .3745 Shaded Area Exaggerated -02 .4207 .4168 .4129 -0.1 .4602 .4562 .4522 Z = -0.21 0.0 .5000 .4960 .4920 © 2002 Prentice-Hall, Inc.

Contoh: Standardized Normal Distribution Normal Distribution Shaded Area Exaggerated © 2002 Prentice-Hall, Inc.

Contoh: (continued) Cumulative Standardized Normal Distribution Table (Portion) Z .00 .01 .02 .6179 0.0 .5000 .5040 .5080 Shaded Area Exaggerated 0.1 .5398 .5438 .5478 0.2 .5793 .5832 .5871 Z = 0.30 0.3 .6179 .6217 .6255 © 2002 Prentice-Hall, Inc.

Mengetahui nilai Z pada Probabilitas tertentu Cumulative Standardized Normal Distribution Table (Portion) What is Z Given Probability = 0.1217 ? .01 Z .00 0.2 0.0 .5000 .5040 .5080 .6217 0.1 .5398 .5438 .5478 0.2 .5793 .5832 .5871 0.3 .6179 .6217 .6255 Shaded Area Exaggerated © 2002 Prentice-Hall, Inc.

Nilai X untuk mengetahui Probabilitas Standardized Normal Distribution Normal Distribution © 2002 Prentice-Hall, Inc.

Normal Probability Plot for Normal Distribution Assessing Normality (continued) Normal Probability Plot for Normal Distribution 90 X 60 30 Z -2 -1 1 2 Look for Straight Line! © 2002 Prentice-Hall, Inc.

Normal Probability Plot Left-Skewed Right-Skewed 90 90 X 60 X 60 30 Z 30 Z -2 -1 1 2 -2 -1 1 2 Rectangular U-Shaped 90 90 X 60 X 60 30 Z 30 Z -2 -1 1 2 -2 -1 1 2 © 2002 Prentice-Hall, Inc.

Larger sample size P(X) Smaller sample size © 2002 Prentice-Hall, Inc.

Populasi Normal Population Distribution Central Tendency Variation Sampling Distributions Sampling with Replacement © 2002 Prentice-Hall, Inc.

Populasi tidak Normal Population Distribution Central Tendency Variation Sampling Distributions Sampling with Replacement © 2002 Prentice-Hall, Inc.

Central Limit Theorem the sampling distribution becomes almost normal regardless of shape of population As sample size gets large enough… © 2002 Prentice-Hall, Inc.

Standardized Normal Distribution Contoh: Standardized Normal Distribution Sampling Distribution © 2002 Prentice-Hall, Inc.