Probability Calculations in Statistics
Characteristics of Normal Distribution
* Bell shaped curve
* Single peak
* Symmetrical mean
* Unlimited number of normal curves
* With different mean and standard deviation
Calculations of Normal Probability Distribution.
The count of a given yarn is found to be normally distributed with a mean of 20 Tex and standard deviation of 3. Using the standard normal table calculate.
01.The percentage of yarn with count greater than 22 tex.
Z = [(x-µ)/ơ]
= (22- 200)/3
=0.6666
From the table = 0.2454
= 0.5 – 0.2454
= 0.2546
Percentage = 0.2546 *
100%
= 25.46%
02.The percentage of yarns count between 17-23
Z1 = [(x1-µ)/ơ]
= (17-20)/3
= -1
= 0.3413
Z2 = [(x2-µ)/ơ]
= (23-20)/3
= 1
=0.3413
= Z1 + Z2
= 0.3413 + 0.3413
= 0.6826
Percentage = 0.6825 * 100%
= 68.26%
03.In a sample of 200 bobbins, the numbers of bobbins with
count less than 19
Z = [(x-µ)/ơ]
= (19 – 20)/3
= -0.3333
From the table = 0.1293
= 0.5 – 0.1293
= 0.3707
For 200 bobbins = 0.3707 * 200
=74.14
=74
Characteristics of
Binomial Distribution
* Discrete probability
distribution
* Each outcome can take only one of the two forms
* The data collected
are the result of counts
Calculations of Binomial Probability Distribution.
Based on experience, 5 percent of the buttons produced by an
automatic button- manufacturing machine are defective. What is the probability
that out of six buttons.
Exactly zero button will be defective?
P=5% , Q=95% , n=6 buttons , r=0!
Pr(r) = [n! /(r! (n-r)!) ] * Prqn-r
Pr(r) = [6! /(0! (6-0)!) ] * (0.05)0*
(0.95)6-0
=0.735
Exactly one button will be defective?
= 0.2321
Exactly two buttons will be defective?
= 0.0354