...Pages
C H A P T E
R
6
The NormalDistribution
Objectives
Outline
After completing this chapter, you should be able to
1
2
3
Identify distributions as symmetric or skewed.
4
Find probabilities for a normally distributed
variable by transforming it into a standardnormal variable.
Introduction
6–1
NormalDistributions
Identify the...

...
NormalDistributionNormaldistribution is a statistics, which have been widely applied of all mathematical concepts, among large number of statisticians. Abraham de Moivre, an 18th century statistician and consultant to gamblers, noticed that as the number of events (N) increased, the distribution approached, forming a very smooth curve.
He insisted that a new discovery of a...

...Deﬁnition 1. A standard (one-dimensional) Wiener process (also called Brownian motion) is
a stochastic process {Wt }t≥0+ indexed by nonnegative real numbers t with the following
properties:
(1)
(2)
(3)
(4)
W0 = 0.
With probability 1, the function t → Wt is continuous in t.
The process {Wt }t≥0 has stationary, independent increments.
The increment Wt+s − Ws has the N ORMAL(0, t) distribution.
A Wiener process with initial value W0 = x is...

...Marks: 1
Assume that X has a normaldistribution, and find the indicated probability.
The mean is μ = 60.0 and the standard deviation is σ = 4.0.
Find the probability that X is less than 53.0.
Choose one answer.
a. 0.5589
b. 0.0401
c. 0.9599
d. 0.0802
Question2
Marks: 1
Use the given degree of confidence and sample data to find a confidence interval for the population standard deviation. Assume that the...

...NormalDistribution:- A continuous random variable X is a normaldistribution with the parameters mean and variance then the probability function can be written as
f(x) = - < x < , - < μ < , σ > 0.
When σ2 = 1, μ = 0 is called as standardnormal.
Normaldistribution problems and solutions – Formulas:
X < μ = 0.5 – Z
X > μ = 0.5 + Z
X = μ = 0.5...

...( 4 decimal places)
2. Find the value of z if the area under a StandardNormal curve
a) to the right of z is 0.3632;
b) to the left of z is 0.1131;
c) between 0 and z, with z > 0, is 0.4838;
d) between -z and z, with z > 0, is 0.9500.
Ans : a) z = + 0.35 ( find 0.5- 0.3632 = 0.1368 in the normal table)
b) z = -1.21 ( find 0.5 – 0.1131 = 0.3869 in the normal table)
c ) the...

...NormalDistribution
It is important because of Central Limit Theorem (CTL), the CTL said that Sum up a lot of i.i.d random variables the shape of the distribution will looks like Normal.
Normal P.D.F
Now we want to find c
This integral has been proved that it cannot have close form solution. However, someone gives an idea that looks stupid but actually very brilliant by multiply two of them.
reminds the...

...the z values.
σ = 3 0.95 σ = 1 0.95
X
19 25 31 -2 0 +2
Normal curve showing Standardnormal curve showing
area between 19 and 31 area between -2 and +2
Entry to a certain University is determined by a national test. The scores on this test are normally distributed with a mean of 500 and a standard deviation of 100.
Tom wants to be admitted to this...

347 Words |
2 Pages

Share this Document

{"hostname":"studymode.com","essaysImgCdnUrl":"\/\/images-study.netdna-ssl.com\/pi\/","useDefaultThumbs":true,"defaultThumbImgs":["\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_1.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_2.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_3.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_4.png","\/\/stm-study.netdna-ssl.com\/stm\/images\/placeholders\/default_paper_5.png"],"thumb_default_size":"160x220","thumb_ac_size":"80x110","isPayOrJoin":false,"essayUpload":false,"site_id":1,"autoComplete":false,"isPremiumCountry":false,"userCountryCode":"US","logPixelPath":"\/\/www.smhpix.com\/pixel.gif","tracking_url":"\/\/www.smhpix.com\/pixel.gif","cookies":{"unlimitedBanner":"off"},"essay":{"essayId":36681769,"categoryName":"Periodicals","categoryParentId":"17","currentPage":1,"format":"text","pageMeta":{"text":{"startPage":1,"endPage":50,"pageRange":"1-50","totalPages":1960}},"access":"premium","title":"Cumulative Properties for the Standard Normal Distribution","additionalIds":[3,7,5,52],"additional":["Business \u0026 Economy","Education","Computer Science","Business \u0026 Economy\/Organizations"],"loadedPages":{"html":[],"text":[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50]}},"user":null,"canonicalUrl":"http:\/\/www.studymode.com\/essays\/Cumulative-Properties-For-The-Standard-Normal-1302535.html","pagesPerLoad":50,"userType":"member_guest","ct":10,"ndocs":"1,500,000","pdocs":"6,000","cc":"10_PERCENT_1MO_AND_6MO","signUpUrl":"https:\/\/www.studymode.com\/signup\/","joinUrl":"https:\/\/www.studymode.com\/join","payPlanUrl":"\/checkout\/pay","upgradeUrl":"\/checkout\/upgrade","freeTrialUrl":"https:\/\/www.studymode.com\/signup\/?redirectUrl=https%3A%2F%2Fwww.studymode.com%2Fcheckout%2Fpay%2Ffree-trial\u0026bypassPaymentPage=1","showModal":"get-access","showModalUrl":"https:\/\/www.studymode.com\/signup\/?redirectUrl=https%3A%2F%2Fwww.studymode.com%2Fjoin","joinFreeUrl":"\/essays\/?newuser=1","siteId":1,"facebook":{"clientId":"306058689489023","version":"v2.8","language":"en_US"},"analytics":{"googleId":"UA-32718321-1"}}