![Yuii](/avatars/23917.jpg)
Yuii
14.07.2019 •
Mathematics
Acompany produces precision 1 meter (1000 mm) rulers. the actual distribution of lengths of the rulers produced by this company is normal, with mean μ and standard deviation σ = 0.02 mm. suppose i select a simple random sample of four of the rulers produced by the company and i measure their lengths in mm. the sample yields = 1000. a 90% confidence interval for μ is:
Solved
Show answers
More tips
- H Health and Medicine Kinesiology: What is it and How Does it Work?...
- O Other How to Choose the Best Answer to Your Question on The Grand Question ?...
- L Leisure and Entertainment History of International Women s Day: When Did the Celebration of March 8th Begin?...
- S Style and Beauty Intimate Haircut: The Reasons, Popularity, and Risks...
- A Art and Culture When Will Eurovision 2011 Take Place?...
- S Style and Beauty How to Choose the Perfect Hair Straightener?...
- F Family and Home Why Having Pets at Home is Good for Your Health...
- H Health and Medicine How to perform artificial respiration?...
- H Health and Medicine 10 Tips for Avoiding Vitamin Deficiency...
- F Food and Cooking How to Properly Cook Buckwheat?...
Answers on questions: Mathematics
- M Mathematics Whats the area of a triangle if all the sides measure to be 8cm...
- M Mathematics F(x)= x^2 -11x -12 in factored form...
- M Mathematics These two figures are the image and pre-image of a dilation. find the length of the missing sides....
- M Mathematics Louis wants groups of 6 daisies and 8 tulips for flower arrangements. he already has 24 daises. how many tulips will he need?...
- M Mathematics Cell company 1 charges $350 for a phone and a monthy bill of $87.50 . cell company 2 charges $200 for a phone and a monthly bill of $92.45 . how many months can you have...
- M Mathematics Multiply using partial products 59x38...
- M Mathematics You owe $1,000 on a credit card that has an interest rate of 27.99% and make only the minimum payment of $20 each month. which answer is correct? a. you will have the card...
- M Mathematics What is 3x+5x+2 factorised for yr 10 gcse...
- M Mathematics Rebecca baked 100 cookies for the state fair 60 were oatmeal 20 were lemon and 20 were chocolate. what percentage of cookies were not oatmeal...
- M Mathematics Write y=2/3x+7 in standard form,a) -2x+3y=21b) -2x-3y=21c) 3x-2y=21d) -2x+3y=7i ve been trying to figure this out but for some reason my answers end up slightly off and...
Ответ:
Let X be the length of rulers. X follows Normal distribution with mean μ and standard deviation σ = 0.02. A sample of size n=4 is drawn from population and sample mean m=1000. We have to find 90% confidence interval for population mean μ.
Here population standard deviation is given to us so we will use z confidence interval for mean. It is given as
(Sample mean - Margin of error , Sample mean + Margin of error)
Where margin of error for z confidence interval is
ME = σ![\frac{z_{\alpha/2}}{\sqrt{n}}](/tpl/images/0089/8137/742ff.png)
Where σ = population standard deviation = 0.02
n= sample size =4
We have to find here 90% confidence interval so confidence level c= 0.9
α = 1 -c =1-0.9 = 0.1
Here we have to find z score value such that area below it is -z is 0.05 and above z is 0.05
Using excel function to find z score value
=NORM.S.INV(0.05) = -1.645
For calculating confidence interval we consider positive z score value which is 1.645
So the margin of error is
ME =![\frac{0.02 * 1.645}{\sqrt{4}}](/tpl/images/0089/8137/ce6b4.png)
ME = 0.01645
90% confidence interval for mean is
(Sample mean - ME, Sample mean+ME)
1000- 0.01645, 1000+0.01645
(1000.01645, 999.9836)
Rounding interval upto 3 decimal places
(1000.016, 999.984)
90% confidence interval for population mean is (1000.016, 999.984)
Ответ: