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For each problem:

  • In words, define the Random Variable X size 12{X} {} .
  • List the values that X may take on.
  • Give the distribution of X . X ~
Then, answer the questions specific to each individual problem.

Six different colored dice are rolled. Of interest is the number of dice that show a “1.”

  • On average, how many dice would you expect to show a “1”?
  • Find the probability that all six dice show a “1.”
  • Is it more likely that 3 or that 4 dice will show a “1”? Use numbers to justify your answer numerically.
  • X size 12{X} {} = the number of dice that show a 1
  • 0,1,2,3,4,5,6
  • X ~ B ( 6 , 1 6 )
  • 1
  • 0.00002
  • 3 dice

More than 96 percent of the very largest colleges and universities (more than 15,000 total enrollments) have some online offerings. Suppose you randomly pick 13 such institutions. We are interested in the number that offer distance learning courses. (Source: http://en.wikipedia.org/wiki/Distance_education)

  • On average, how many schools would you expect to offer such courses?
  • Find the probability that at most 6 offer such courses.
  • Is it more likely that 0 or that 13 will offer such courses? Use numbers to justify your answer numerically and answer in a complete sentence.

A school newspaper reporter decides to randomly survey 12 students to see if they will attend Tet (Vietnamese New Year) festivities this year. Based on past years, she knows that 18% of students attend Tet festivities. We are interested in the number of students who will attend the festivities.

  • How many of the 12 students do we expect to attend the festivities?
  • Find the probability that at most 4 students will attend.
  • Find the probability that more than 2 students will attend.
  • X size 12{X} {} = the number of students that will attend Tet.
  • 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12
  • X ~ B(12,0.18)
  • 2.16
  • 0.9511
  • 0.3702

Suppose that about 85% of graduating students attend their graduation. A group of 22 graduating students is randomly chosen.

  • How many are expected to attend their graduation?
  • Find the probability that 17 or 18 attend.
  • Based on numerical values, would you be surprised if all 22 attended graduation? Justify your answer numerically.

At The Fencing Center, 60% of the fencers use the foil as their main weapon. We randomly survey 25 fencers at The Fencing Center. We are interested in the numbers that do not use the foil as their main weapon.

  • How many are expected to not use the foil as their main weapon?
  • Find the probability that six do not use the foil as their main weapon.
  • Based on numerical values, would you be surprised if all 25 did not use foil as their main weapon? Justify your answer numerically.
  • X size 12{X} {} = the number of fencers that do not use foil as their main weapon
  • 0, 1, 2, 3,... 25
  • X ~ B(25,0.40)
  • 10
  • 0.0442
  • Yes

Approximately 8% of students at a local high school participate in after-school sports all four years of high school. A group of 60 seniors is randomly chosen. Of interest is the number that participated in after-school sports all four years of high school.

  • How many seniors are expected to have participated in after-school sports all four years of high school?
  • Based on numerical values, would you be surprised if none of the seniors participated in after-school sports all four years of high school? Justify your answer numerically.
  • Based upon numerical values, is it more likely that 4 or that 5 of the seniors participated in after-school sports all four years of high school? Justify your answer numerically.

Questions & Answers

what is biology
Hajah Reply
the study of living organisms and their interactions with one another and their environments
AI-Robot
what is biology
Victoria Reply
HOW CAN MAN ORGAN FUNCTION
Alfred Reply
the diagram of the digestive system
Assiatu Reply
allimentary cannel
Ogenrwot
How does twins formed
William Reply
They formed in two ways first when one sperm and one egg are splited by mitosis or two sperm and two eggs join together
Oluwatobi
what is genetics
Josephine Reply
Genetics is the study of heredity
Misack
how does twins formed?
Misack
What is manual
Hassan Reply
discuss biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles
Joseph Reply
what is biology
Yousuf Reply
the study of living organisms and their interactions with one another and their environment.
Wine
discuss the biological phenomenon and provide pieces of evidence to show that it was responsible for the formation of eukaryotic organelles in an essay form
Joseph Reply
what is the blood cells
Shaker Reply
list any five characteristics of the blood cells
Shaker
lack electricity and its more savely than electronic microscope because its naturally by using of light
Abdullahi Reply
advantage of electronic microscope is easily and clearly while disadvantage is dangerous because its electronic. advantage of light microscope is savely and naturally by sun while disadvantage is not easily,means its not sharp and not clear
Abdullahi
cell theory state that every organisms composed of one or more cell,cell is the basic unit of life
Abdullahi
is like gone fail us
DENG
cells is the basic structure and functions of all living things
Ramadan
What is classification
ISCONT Reply
is organisms that are similar into groups called tara
Yamosa
in what situation (s) would be the use of a scanning electron microscope be ideal and why?
Kenna Reply
A scanning electron microscope (SEM) is ideal for situations requiring high-resolution imaging of surfaces. It is commonly used in materials science, biology, and geology to examine the topography and composition of samples at a nanoscale level. SEM is particularly useful for studying fine details,
Hilary
cell is the building block of life.
Condoleezza Reply
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Source:  OpenStax, Collaborative statistics for mt230. OpenStax CNX. Aug 18, 2011 Download for free at http://legacy.cnx.org/content/col11345/1.2
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