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A pharmaceutical company makes tranquilizers. It is assumed that the distribution for the length of time they last is approximately normal. Researchers in a hospital used the drug on a random sample of 9 patients. The effective period of the tranquilizer for each patient (in hours) was as follows: 2.7; 2.8; 3.0; 2.3; 2.3; 2.2; 2.8; 2.1; and 2.4 .

    • x ¯ = size 12{ {overline {x}} ={}} {} ________
    • s x = size 12{s rSub { size 8{x} } ={}} {} ________
    • n = size 12{n} {} ________
    • n 1 = size 12{n - 1} {} ________
  • Define the Random Variable X size 12{X} {} , in words.
  • Define the Random Variable X ¯ size 12{ {overline {X}} } {} , in words.
  • Which distribution should you use for this problem? Explain your choice.
  • Construct a 95% confidence interval for the population mean length of time.
    • State the confidence interval.
    • Sketch the graph.
    • Calculate the error bound.
  • What does it mean to be “95% confident” in this problem?

Suppose that 14 children were surveyed to determine how long they had to use training wheels. It was revealed that they used them an average of 6 months with a sample standard deviation of 3 months. Assume that the underlying population distribution is normal.

    • x ¯ = size 12{ {overline {x}} ={}} {} ________
    • s x = size 12{s rSub { size 8{x} } ={}} {} ________
    • n = size 12{n} {} ________
    • n 1 = size 12{n - 1} {} ________
  • Define the Random Variable X size 12{X} {} , in words.
  • Define the Random Variable X ¯ size 12{ {overline {X}} } {} , in words.
  • Which distribution should you use for this problem? Explain your choice.
  • Construct a 99% confidence interval for the population mean length of time using training wheels.
    • State the confidence interval.
    • Sketch the graph.
    • Calculate the error bound.
  • Why would the error bound change if the confidence level was lowered to 90%?

    • 6
    • 3
    • 14
    • 13
  • the time for a child to remove his training wheels
  • the mean time for 14 children to remove their training wheels.
  • t 13 size 12{t rSub { size 8{"13"} } } {}
    • CI: (3.58, 8.42)
    • EB = 2.42

Insurance companies are interested in knowing the population percent of drivers who always buckle up before riding in a car.

  • When designing a study to determine this population proportion, what is the minimum number you would need to survey to be 95% confident that the population proportion is estimated to within 0.03?
  • If it was later determined that it was important to be more than 95% confident and a new survey was commissioned, how would that affect the minimum number you would need to survey? Why?

Suppose that the insurance companies did do a survey. They randomly surveyed 400 drivers and found that 320 claimed to always buckle up. We are interested in the population proportion of drivers who claim to always buckle up.

    • x = size 12{x} {} ________
    • n = size 12{n} {} ________
    • p ' = size 12{p'} {} ________
  • Define the Random Variables X size 12{X} {} and P ' size 12{P'} {} , in words.
  • Which distribution should you use for this problem? Explain your choice.
  • Construct a 95% confidence interval for the population proportion that claim to always buckle up.
    • State the confidence interval.
    • Sketch the graph.
    • Calculate the error bound.
  • If this survey were done by telephone, list 3 difficulties the companies might have in obtaining random results.

    • 320
    • 400
    • 0.80
  • N ( 0.80 , (0.80)(0.20) 400 )
    • CI: (0.76, 0.84)
    • EB = 0.04

Unoccupied seats on flights cause airlines to lose revenue. Suppose a large airline wants to estimate its mean number of unoccupied seats per flight over the past year. To accomplish this, the records of 225 flights are randomly selected and the number of unoccupied seats is noted for each of the sampled flights. The sample mean is 11.6 seats and the sample standard deviation is 4.1 seats.

    • x ¯ = size 12{ {overline {x}} ={}} {} ________
    • s x = size 12{s rSub { size 8{x} } ={}} {} ________
    • n = size 12{n} {} ________
    • n 1 = size 12{n - 1} {} ________
  • Define the Random Variables X size 12{X} {} and X ¯ size 12{ {overline {X}} } {} , in words.
  • Which distribution should you use for this problem? Explain your choice.
  • Construct a 92% confidence interval for the population mean number of unoccupied seats per flight.
    • State the confidence interval.
    • Sketch the graph.
    • Calculate the error bound.

Questions & Answers

how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
ninjadapaul
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
ninjadapaul
I don't understand what the A with approx sign and the boxed x mean
ninjadapaul
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
ninjadapaul
oops. ignore that.
ninjadapaul
so you not have an equal sign anywhere in the original equation?
ninjadapaul
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
AMJAD
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
AMJAD
what is system testing
AMJAD
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Elementary statistics. OpenStax CNX. Dec 30, 2013 Download for free at http://cnx.org/content/col10966/1.4
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