<< Chapter < Page Chapter >> Page >
In this module the student will explore the properties of data with a uniform distribution.

Student learning outcomes

  • The student will analyze data following a uniform distribution.

Given

The age of cars in the staff parking lot of a suburban college is uniformly distributed from six months (0.5 years) to 9.5 years.

Describe the data

What is being measured here?

The age of cars in the staff parking lot

Got questions? Get instant answers now!

In words, define the Random Variable X size 12{X} {} .

X size 12{X} {} = The age (in years) of cars in the staff parking lot

Got questions? Get instant answers now!

Are the data discrete or continuous?

Continuous

Got questions? Get instant answers now!

The interval of values for x size 12{X} {} is:

0.5 - 9.5

Got questions? Get instant answers now!

The distribution for X size 12{X} {} is:

X size 12{X} {} ~ U ( 0 . 5,9 . 5 ) size 12{U \( 0 "." 5,9 "." 5 \) } {}

Got questions? Get instant answers now!

Probability distribution

Write the probability density function.

f ( x ) size 12{f \( x \) } {} = 1 9 size 12{ { {1} over {9} } } {}

Got questions? Get instant answers now!

Graph the probability distribution.

  • Sketch the graph of the probability distribution.
  • Identify the following values:
    • Lowest value for x size 12{X} {} :
    • Highest value for x size 12{X} {} :
    • Height of the rectangle:
    • Label for x-axis (words):
    • Label for y-axis (words):
  • 0.5
  • 9.5
  • 1 9 size 12{ { {1} over {9} } } {}
  • Age of Cars
  • f ( x ) size 12{f \( x \) } {}
Got questions? Get instant answers now!

Random probability

Find the probability that a randomly chosen car in the lot was less than 4 years old.

  • Sketch the graph. Shade the area of interest.
    Blank graph with vertical and horizontal axes.
  • Find the probability. P ( x < 4 ) size 12{P \( X<"5730" \) } {} =
  • 3 . 5 9 size 12{ { {3 "." 5} over {9} } } {}
Got questions? Get instant answers now!

Out of just the cars less than 7.5 years old, find the probability that a randomly chosen car in the lot was less than 4 years old.

  • Sketch the graph. Shade the area of interest.
  • Find the probability. P ( x < 4 x < 7 . 5 ) size 12{P \( X<4 \lline X<7 "." 5 \) } {} =
  • 3 . 5 7 size 12{ { {3 "." 5} over {7} } } {}
Got questions? Get instant answers now!

What has changed in the previous two problems that made the solutions different?

Got questions? Get instant answers now!

Quartiles

Find the average age of the cars in the lot.

μ size 12{μ} {} = 5

Got questions? Get instant answers now!

Find the third quartile of ages of cars in the lot. This means you will have to find the value such that 3 4 size 12{ { {3} over {4} } } {} , or 75%, of the cars are at most (less than or equal to) that age.

  • Sketch the graph. Shade the area of interest.
    Blank graph with vertical and horizontal axes.
  • Find the value k size 12{k} {} such that P ( x < k ) = 0 . 75 size 12{P \( X<k \) =0 "." "75"} {} .
  • The third quartile is:
  • k size 12{k} {} = 7.25
Got questions? Get instant answers now!

Questions & Answers

what is mutation
Janga Reply
what is a cell
Sifune Reply
how is urine form
Sifune
what is antagonism?
mahase Reply
classification of plants, gymnosperm features.
Linsy Reply
what is the features of gymnosperm
Linsy
how many types of solid did we have
Samuel Reply
what is an ionic bond
Samuel
What is Atoms
Daprince Reply
what is fallopian tube
Merolyn
what is bladder
Merolyn
what's bulbourethral gland
Eduek Reply
urine is formed in the nephron of the renal medulla in the kidney. It starts from filtration, then selective reabsorption and finally secretion
onuoha Reply
State the evolution relation and relevance between endoplasmic reticulum and cytoskeleton as it relates to cell.
Jeremiah
what is heart
Konadu Reply
how is urine formed in human
Konadu
how is urine formed in human
Rahma
what is the diference between a cavity and a canal
Pelagie Reply
what is the causative agent of malaria
Diamond
malaria is caused by an insect called mosquito.
Naomi
Malaria is cause by female anopheles mosquito
Isaac
Malaria is caused by plasmodium Female anopheles mosquitoe is d carrier
Olalekan
a canal is more needed in a root but a cavity is a bad effect
Commander
what are pathogens
Don Reply
In biology, a pathogen (Greek: πάθος pathos "suffering", "passion" and -γενής -genēs "producer of") in the oldest and broadest sense, is anything that can produce disease. A pathogen may also be referred to as an infectious agent, or simply a germ. The term pathogen came into use in the 1880s.[1][2
Zainab
A virus
Commander
Definition of respiration
Muhsin Reply
respiration is the process in which we breath in oxygen and breath out carbon dioxide
Achor
how are lungs work
Commander
where does digestion begins
Achiri Reply
in the mouth
EZEKIEL
what are the functions of follicle stimulating harmones?
Rashima Reply
stimulates the follicle to release the mature ovum into the oviduct
Davonte
what are the functions of Endocrine and pituitary gland
Chinaza
endocrine secrete hormone and regulate body process
Achor
while pituitary gland is an example of endocrine system and it's found in the Brain
Achor
what's biology?
Egbodo Reply
Biology is the study of living organisms, divided into many specialized field that cover their morphology, physiology,anatomy, behaviour,origin and distribution.
Lisah
biology is the study of life.
Alfreda
Biology is the study of how living organisms live and survive in a specific environment
Sifune
Got questions? Join the online conversation and get instant answers!
Jobilize.com Reply

Get Jobilize Job Search Mobile App in your pocket Now!

Get it on Google Play Download on the App Store Now




Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'Collaborative statistics' conversation and receive update notifications?

Ask