Normal distribution and intro to continuous probability density functions... www.stat.psu.edu/~resources/ClassNotes/lj s_08/ljs_08.PPT -

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1 Normal distribution and intro to continuous probability density functions... www.stat.psu.edu/~resources/ClassNotes/lj s_08/ljs_08.PPT -

2 Percent Histogram

3 Histogram (Area of rectangle = probability)

4 Decrease interval size...

5 Decrease interval size more….

6 Continuous probability density 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 normal random 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 Table p. 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 : 1.MUTUALLY EXCLUSIVE, PROBABILITAS SUKSES & GAGAL 2.INDEPENDEN 3.P BERNILAI TETAP 4...np dan n (1-p) harus lebih besar dari 5 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 ; 1.DARI 200 PENCURIAN BARANG, TENTUKAN PROBABILITAS 170 KASUS PENCURIAN BARANG ATAU LEBIH DAPAT KEMBALI 2.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?