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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

what is math number
Tric Reply
x-2y+3z=-3 2x-y+z=7 -x+3y-z=6
Sidiki Reply
Need help solving this problem (2/7)^-2
Simone Reply
x+2y-z=7
Sidiki
what is the coefficient of -4×
Mehri Reply
-1
Shedrak
the operation * is x * y =x + y/ 1+(x × y) show if the operation is commutative if x × y is not equal to -1
Alfred Reply
An investment account was opened with an initial deposit of $9,600 and earns 7.4% interest, compounded continuously. How much will the account be worth after 15 years?
Kala Reply
lim x to infinity e^1-e^-1/log(1+x)
given eccentricity and a point find the equiation
Moses Reply
12, 17, 22.... 25th term
Alexandra Reply
12, 17, 22.... 25th term
Akash
College algebra is really hard?
Shirleen Reply
Absolutely, for me. My problems with math started in First grade...involving a nun Sister Anastasia, bad vision, talking & getting expelled from Catholic school. When it comes to math I just can't focus and all I can hear is our family silverware banging and clanging on the pink Formica table.
Carole
I'm 13 and I understand it great
AJ
I am 1 year old but I can do it! 1+1=2 proof very hard for me though.
Atone
hi
Adu
Not really they are just easy concepts which can be understood if you have great basics. I am 14 I understood them easily.
Vedant
find the 15th term of the geometric sequince whose first is 18 and last term of 387
Jerwin Reply
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
virgelyn Reply
hmm well what is the answer
Abhi
If f(x) = x-2 then, f(3) when 5f(x+1) 5((3-2)+1) 5(1+1) 5(2) 10
Augustine
how do they get the third part x = (32)5/4
kinnecy Reply
make 5/4 into a mixed number, make that a decimal, and then multiply 32 by the decimal 5/4 turns out to be
AJ
how
Sheref
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
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
Commplementary angles
Idrissa Reply
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
hi
salma
hi
Ayuba
Hello
opoku
hi
Ali
greetings from Iran
Ali
salut. from Algeria
Bach
hi
Nharnhar
A soccer field is a rectangle 130 meters wide and 110 meters long. The coach asks players to run from one corner to the other corner diagonally across. What is that distance, to the nearest tenths place.
Kimberly Reply
Jeannette has $5 and $10 bills in her wallet. The number of fives is three more than six times the number of tens. Let t represent the number of tens. Write an expression for the number of fives.
August Reply
What is the expressiin for seven less than four times the number of nickels
Leonardo Reply
How do i figure this problem out.
how do you translate this in Algebraic Expressions
linda Reply
why surface tension is zero at critical temperature
Shanjida
I think if critical temperature denote high temperature then a liquid stats boils that time the water stats to evaporate so some moles of h2o to up and due to high temp the bonding break they have low density so it can be a reason
s.
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
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Source:  OpenStax, Collaborative statistics homework book: custom version modified by r. bloom. OpenStax CNX. Dec 23, 2009 Download for free at http://legacy.cnx.org/content/col10619/1.2
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