The Continuous Probability Distribution.pdf

Summarize the probability without any continuity

1. Continuous Probability
Distributions
Lecturer
K M Muhaiminul Nafiu
AhsanullahUniversity of Science and Technology

2. Continuous Variable
•A continuous random variable can assume any value over an interval or
intervals

3. Probability Sums

4. •The Normal Distribution
•A large number of phenomena in the real world are approximately
normally distributed.
Thecontinuousrandomvariablesrepresentingheightsandweightsof
people,scoresonanexamination,weightsofpackages(e.g.,cereal
boxes,boxesofcookies),amountofmilkinagallon,lifeofanitem
(suchasalight-bulboratelevisionset),andtimetakentocompletea
certainjobhaveallbeenobservedtohaveanapproximatenormal
distribution.

6. Normal Distribution

8. The Standard Normal Distribution

9. Standardizing a Normal Distribution

10. Thezvaluesontherightsideofthemeanarepositiveandthoseontheleftsidearenegative.Thezvaluefora
pointonthehorizontalaxisgivesthedistancebetweenthemeanandthatpointintermsofthestandarddeviation.
For example, a point with a value of Z = 2 is two standard deviations to the right of the mean. Similarly, a
point with a value of Z =-2 is two standard deviations to the left of the mean.

13. AracingcarisoneofthemanytoysmanufacturedbyMackCorporation.Theassembly
timesforthistoyfollowanormaldistributionwithameanof55minutesandastandard
deviationof4minutes.Thecompanyclosesat5P.M.everyday.Ifoneworkerstartsto
assemblearacingcarat4P.M.,whatistheprobabilitythatshewillfinishthisjobbefore
thecompanyclosesfortheday?

20. Exponential Distribution

21. Exponential Distribution

22. Exponential Distribution