1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Artemon [7]
2 years ago
8

A laboratory scale is known to have a standard deviation (sigma) or 0.001 g in repeated weighings. Scale readings in repeated we

ighings are Normally distributed with mean equal to the true weight of the specimen. Three weighings of a specimen on this scale give 3.412, 3.416, and 3.414 g. A 99% confidence interval for this specimen is:
Mathematics
1 answer:
weqwewe [10]2 years ago
6 0

Answer:

99% confidence interval for the given specimen is [3.4125 , 3.4155].

Step-by-step explanation:

We are given that a laboratory scale is known to have a standard deviation (sigma) or 0.001 g in repeated weighing. Scale readings in repeated weighing are Normally distributed with mean equal to the true weight of the specimen.

Three weighing of a specimen on this scale give 3.412, 3.416, and 3.414 g.

Firstly, the pivotal quantity for 99% confidence interval for the true mean specimen is given by;

        P.Q. = \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } } ~ N(0,1)

where, \bar X = sample mean weighing of specimen = \frac{3.412+3.416+3.414}{3} = 3.414 g

            \sigma = population standard deviation = 0.001 g

            n = sample of specimen = 3

            \mu = population mean

<em>Here for constructing 99% confidence interval we have used z statistics because we know about population standard deviation (sigma).</em>

So, 99% confidence interval for the population​ mean, \mu is ;

P(-2.5758 < N(0,1) < 2.5758) = 0.99  {As the critical value of z at 0.5% level

                                                            of significance are -2.5758 & 2.5758}

P(-2.5758 < \frac{\bar X - \mu}{\frac{\sigma}{\sqrt{n} } } < 2.5758) = 0.99

P( -2.5758 \times {\frac{\sigma}{\sqrt{n} } } < {\bar X - \mu} < 2.5758 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.99

P( \bar X-2.5758 \times {\frac{\sigma}{\sqrt{n} } } < \mu < \bar X+2.5758 \times {\frac{\sigma}{\sqrt{n} } } ) = 0.99

<u>99% confidence interval for</u> \mu = [ \bar X-2.5758 \times {\frac{\sigma}{\sqrt{n} } } , \bar X+2.5758 \times {\frac{\sigma}{\sqrt{n} } } ]

                                             = [ 3.414-2.5758 \times {\frac{0.001}{\sqrt{3} } } , 3.414+2.5758 \times {\frac{0.001}{\sqrt{3} } } ]

                                             = [3.4125 , 3.4155]

Therefore, 99% confidence interval for this specimen is [3.4125 , 3.4155].

You might be interested in
Another one lol(picture)
Andreyy89
Look up the law of sines, I suggest Khan Academy. It is better if you know how to do it, it is very useful.
7 0
3 years ago
Simplify ((1/x)-(1/y))/((1/x)+(1/y))
In-s [12.5K]
<span>Simplify ((1/x)-(1/y))/((1/x)+(1/y))</span>


y-x
______

y+x
7 0
3 years ago
What number equals 2/9?​
kati45 [8]
So I would say 4/18 but it could probably be 18/81 to
3 0
2 years ago
What’s the answers to 13, 14, 14, and 16???
abruzzese [7]

For number 13,the arrow should be going “<“ way because it is in fraction form and the bigger the number the smaller the pieces. This repeats for the rest of the questions so for number 14,the answer is “=“,and for number 15 it is “>”
6 0
3 years ago
Brian rented a truck for one day. there was a base fee of $18.99 , and there was an additional charge of 75 cents for each mile
Taya2010 [7]
He drove 122 miles
hope this helps :)
4 0
3 years ago
Other questions:
  • What is the product of (-a + 3)(a + 4)​
    6·2 answers
  • Slope: 5, y-intercept: -3
    15·1 answer
  • Simplify the following expression. 5(2x -3) + 4( x + 1)
    15·1 answer
  • What is the answer for r?<br> 13=r/9+8
    6·2 answers
  • Which of the following equations represents the same relationship as the graph shown below?
    6·1 answer
  • Please help, I don't want any links​
    9·1 answer
  • You are buying the new iphone 7 that originally costs $299. Verizon is running a sale that all phones are now 30% off. The sales
    12·1 answer
  • Solve this please show your work &lt;3
    12·1 answer
  • Can somebody help me with questions 11 and 12 I’ll appreciate it!
    9·2 answers
  • Which angle is an adjacent interior angle to ∠jkm? ∠jkl ∠mkl ∠klm ∠lmk
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!