<< Chapter < Page Chapter >> Page >

Suppose that a category of world class runners are known to run a marathon (26 miles) in an average of 145 minutes with a standard deviation of 14 minutes. Consider 49 of the races.

Let X ¯ = size 12{ {overline {X}} ={}} {} the average of the 49 races.

  • X ¯ ~ size 12{ {overline {X}} "~" } {}
  • Find the probability that the runner will average between 142 and 146 minutes in these 49 marathons.
  • Find the 80th percentile for the average of these 49 marathons.
  • Find the median of the average running times.
  • N ( 145 , 14 49 ) size 12{ ital "Xbar" "~" N \( "145", { {"14"} over { sqrt {"49"} } } \) } {}
  • 0.6247
  • 146.68
  • 145 minutes

Suppose that the length of research papers is uniformly distributed from 10 to 25 pages. We survey a class in which 55 research papers were turned in to a professor. The 55 research papers are considered a random collection of all papers. We are interested in the average length of the research papers.

  • In words, X = size 12{X={}} {}
  • X ~ size 12{X "~" } {}
  • μ X = size 12{μ rSub { size 8{X} } ={}} {}
  • σ X = size 12{σ rSub { size 8{X} } ={}} {}
  • In words, X ¯ = size 12{ {overline {X}} ={}} {}
  • X ¯ ~ size 12{ {overline {X}} "~" } {}
  • In words, ΣX = size 12{ΣX={}} {}
  • ΣX ~ size 12{ΣX "~" } {}
  • Without doing any calculations, do you think that it’s likely that the professor will need to read a total of more than 1050 pages? Why?
  • Calculate the probability that the professor will need to read a total of more than 1050 pages.
  • Why is it so unlikely that the average length of the papers will be less than 12 pages?
  • U ( 10 , 25 ) size 12{X "~" U \( "10","25" \) } {}
  • 17.5
  • 225 12 = 4.3301
  • N ( 17.5 , 0.5839 ) size 12{X "~" U \( "10","25" \) } {}
  • N ( 962.5 , 32.11 ) size 12{X "~" U \( "10","25" \) } {}
  • 0.0032

The length of songs in a collector’s CD collection is uniformly distributed from 2 to 3.5 minutes. Suppose we randomly pick 5 CDs from the collection. There is a total of 43 songs on the 5 CDs.

  • In words, X = size 12{X={}} {}
  • X ~ size 12{X "~" } {}
  • In words, X ¯ = size 12{ {overline {X}} "~" } {}
  • X ¯ ~ size 12{ {overline {X}} "~" } {}
  • Find the first quartile for the average song length.
  • The IQR (interquartile range) for the average song length is from _______ to _______.

Salaries for teachers in a particular elementary school district are normally distributed with a mean of $44,000 and a standard deviation of $6500. We randomly survey 10 teachers from that district.

  • In words, X = size 12{X={}} {}
  • In words, X ¯ = size 12{ {overline {X}} ={}} {}
  • X ¯ ~ size 12{ {overline {X}} "~" } {}
  • In words, ΣX = size 12{ΣX={}} {}
  • ΣX ~ size 12{ΣX "~" } {}
  • Find the probability that the teachers earn a total of over $400,000.
  • Find the 90th percentile for an individual teacher’s salary.
  • Find the 90th percentile for the average teachers’ salary.
  • If we surveyed 70 teachers instead of 10, graphically, how would that change the distribution for X ¯ size 12{ {overline {X}} } {} ?
  • If each of the 70 teachers received a $3000 raise, graphically, how would that change the distribution for X ¯ size 12{ {overline {X}} } {} ?
  • N ( 44 , 000 , 6500 10 ) size 12{ ital "Xbar" "~" N \( "44","000", { {"6500"} over { sqrt {"10"} } } \) } {}
  • N ( 440,000 , ( 10 ) ( 6500 ) ) size 12{ ital "SumX" "~" N \( "10" * "44","000", sqrt { \( "10" * "6500" \) } \) } {}
  • 0.9742
  • $52,330
  • $46,634

The distribution of income in some Third World countries is not considered normal (many very poor people, very few middle income people, and few to many wealthy people). We pick a country consistent with this non-normal distribution. We find the average salary be $2000 per year with a standard deviation of $8000. We randomly surveyed 1000 residents of that country.

  • In words, X = size 12{X={}} {}
  • In words, X ¯ = size 12{ {overline {X}} ={}} {}
  • X ¯ ~ size 12{ {overline {X}} "~" } {}
  • How is it possible for the standard deviation to be greater than the average?
  • Why is it more likely that the average of the 1000 residents will be from $2000 to $2100 than from $2100 to $2200?

The average length of a maternity stay in a U.S. hospital is said to be 2.4 days with a standard deviation of 0.9 days. We randomly survey 80 women who recently bore children in a U.S. hospital.

  • In words, X = size 12{X={}} {}
  • In words, X ¯ = size 12{ {overline {X}} ={}} {}
  • X ¯ ~ size 12{ {overline {X}} "~" } {}
  • In words, ΣX = size 12{ΣX={}} {}
  • ΣX ~ size 12{ΣX "~" } {}
  • Is it likely that an individual stayed more than 5 days in the hospital? Why or why not?
  • Is it likely that the average stay for the 80 women was more than 5 days? Why or why not?
  • Which is more likely:
    • an individual stayed more than 5 days; or
    • the average stay of 80 women was more than 5 days?
  • If we were to sum up the women’s stays, is it likely that, collectively they spent more than a year in the hospital? Why or why not?
  • N ( 2 . 4, 0 . 9 80 ) size 12{ ital "Xbar" "~" N \( 2 "." 4, { {0 "." 9} over { sqrt {"80"} } } \) } {}
  • N ( 192 , 8.05 ) size 12{ ital "SumX" "~" N \( "80" * 2 "." 4, sqrt {"80"} * 0 "." 9 \) } {}
  • Individual

Questions & Answers

if three forces F1.f2 .f3 act at a point on a Cartesian plane in the daigram .....so if the question says write down the x and y components ..... I really don't understand
Syamthanda Reply
hey , can you please explain oxidation reaction & redox ?
Boitumelo Reply
hey , can you please explain oxidation reaction and redox ?
Boitumelo
for grade 12 or grade 11?
Sibulele
the value of V1 and V2
Tumelo Reply
advantages of electrons in a circuit
Rethabile Reply
we're do you find electromagnetism past papers
Ntombifuthi
what a normal force
Tholulwazi Reply
it is the force or component of the force that the surface exert on an object incontact with it and which acts perpendicular to the surface
Sihle
what is physics?
Petrus Reply
what is the half reaction of Potassium and chlorine
Anna Reply
how to calculate coefficient of static friction
Lisa Reply
how to calculate static friction
Lisa
How to calculate a current
Tumelo
how to calculate the magnitude of horizontal component of the applied force
Mogano
How to calculate force
Monambi
a structure of a thermocouple used to measure inner temperature
Anna Reply
a fixed gas of a mass is held at standard pressure temperature of 15 degrees Celsius .Calculate the temperature of the gas in Celsius if the pressure is changed to 2×10 to the power 4
Amahle Reply
How is energy being used in bonding?
Raymond Reply
what is acceleration
Syamthanda Reply
a rate of change in velocity of an object whith respect to time
Khuthadzo
how can we find the moment of torque of a circular object
Kidist
Acceleration is a rate of change in velocity.
Justice
t =r×f
Khuthadzo
how to calculate tension by substitution
Precious Reply
hi
Shongi
hi
Leago
use fnet method. how many obects are being calculated ?
Khuthadzo
khuthadzo hii
Hulisani
how to calculate acceleration and tension force
Lungile Reply
you use Fnet equals ma , newtoms second law formula
Masego
please help me with vectors in two dimensions
Mulaudzi Reply
how to calculate normal force
Mulaudzi
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 using spreadsheets. OpenStax CNX. Jan 05, 2016 Download for free at http://legacy.cnx.org/content/col11521/1.23
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

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

Ask