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Normal distribution

Normal distribution. and intro to continuous probability density functions... www.stat.psu.edu/~resources/ClassNotes/ljs_08/ljs_08. PPT -. Percent Histogram. Histogram (Area of rectangle = probability). Decrease interval size. Decrease interval size more….

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Normal distribution

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  1. Normal distribution and intro to continuous probability density functions... www.stat.psu.edu/~resources/ClassNotes/ljs_08/ljs_08.PPT -

  2. Percent Histogram

  3. Histogram(Area of rectangle = probability)

  4. Decrease interval size...

  5. Decrease interval size more….

  6. Continuous probabilitydensity functions • The curve describes probability of getting any range of values, say P(X > 120), P(X<100), P(110 < X < 120) • Area under the curve = probability • Area under whole curve = 1 • Probability of getting specific number is 0, e.g. P(X=120) = 0

  7. Special kind of continuous p.d.f

  8. Characteristics of normal distribution • Symmetric, bell-shaped curve. • Shape of curve depends on population mean and standard deviation . • Center of distribution is . • Spread is determined by . • Most values fall around the mean, but some values are smaller and some are larger. • ASIMPTOT

  9. Examples of normalrandom variables • testosterone level of male students • head circumference of adult females • length of middle finger of Stat 250 students

  10. Probability above 75?

  11. Probability = Area under curve • Calculus?! You’re kidding, right? • But somebody did all the hard work for us! • We just need a table of probabilities for every possible normal distribution. • But there are an infinite number of normal distributions (one for each  and )!! • Solution is to “standardize.”

  12. Standardizing • Take value X and subtract its mean  from it, and then divide by its standard deviation . Call the resulting value Z. • That is, Z = (X- )/ • Z is called the standard normal. Its mean  is 0 and standard deviation  is 1. • Then, use probability table for Z.

  13. Using Z Table

  14. Reading Z Tablep. 484, Appendix A • Carry out Z calculations to two decimal places, that is X.XX • Find the first two digits (X.XX) of Z in column headed by z. • Find the third digit of Z (X.XX) in first row. • P(Z > z) = probability found at the intersection of the column and row.

  15. Probability between 65 and 70?

  16. Probability below 65?

  17. Remember! • Calculated probabilities are accurate only if the assumptions made are indeed correct! • When doing the above calculations, you are assuming that the data are “normally distributed.” • Always check this assumption! (We’ll learn how to next class.)

  18. PENDEKATAN NORMAL PADA BINOMIAL • KARAKTERISTIK : • MUTUALLY EXCLUSIVE, PROBABILITAS SUKSES & GAGAL • INDEPENDEN • P BERNILAI TETAP • ..np dan n (1-p) harus lebih besar dari 5 • Ada FAKTOR KOREKSI KONTINUITAS ( FKK) + 0,5 ATAU – 0,5

  19. CONTOH SOAL • DARI DATA SAVE THE HOME MENUNJUKKAN BAHWA PROBABILITA BARANG YANG DICURI DITEMUKAN KEMBALI ADALAH 80 %. TENTUKAN ; • DARI 200 PENCURIAN BARANG , TENTUKAN PROBABILITAS 170 KASUS PENCURIAN BARANG ATAU LEBIH DAPAT KEMBALI • DARI 200 PENCURIAN, TENTUKAN PROBABILITAS 150 KASUS PENCURIAN BARANG ATAU LEBIH DAPAT KEMBALI

  20. Contoh Soal • Diketahui nilai rata-rata hitung UTS Statsos adalah 75 dengan ragam 64. Jika dosen ingin memberikan 10 persen teratas dari nilai ujian tersebut tentukanlah batas kelas tersebut?

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