We appreciate your visit to The volume in a set of wine bottles is known to follow a normal distribution with a mean of tex mu tex ounces and a. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
We need to sample at least 18 wine bottles to construct a 90% confidence interval for the mean volume of the population, with a margin of error of at most 0.1 ounces.
To determine the sample size required for a given confidence interval and margin of error, we need to use the following formula:
[tex]n = (Z^2 * \sigma^2) / E^2[/tex]
Where:
n = sample size
Z = the z-score associated with the desired confidence interval (for 90% confidence, Z = 1.645)
σ = the standard deviation of the population (0.5 ounces in this case)
E = the desired margin of error (0.1 ounces in this case)
Plugging in the values, we get:
[tex]n = (1.645^2 * 0.5^2) / 0.1^2[/tex]
n = 17.1
Thus, we need to sample at least 18 wine bottles to create a 90% confidence interval for the population's mean volume, with a margin of error of no more than 0.1 ounces.
For more details regarding confidence interval, visit:
https://brainly.com/question/24131141
#SPJ1
Thanks for taking the time to read The volume in a set of wine bottles is known to follow a normal distribution with a mean of tex mu tex ounces and a. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
We need to sample at least 69 bottles to construct a 90% confidence interval for the mean volume of the wine bottles with a margin of error at most 0.1 ounces.
We have,
To construct a confidence interval for the mean volume of the wine bottles, we need to use the formula:
Confidence interval = sample mean ± margin of error
Where,
Margin of error = z (σ/√(n))
Here, we want to construct a 90% confidence interval with a margin of error at most 0.1 ounces.
This means that the margin of error should be less than or equal to 0.1, and the confidence level is 90%, so the critical value of z is 1.645
(using a standard normal table or calculator).
We are given that the standard deviation is σ = 0.5 ounces.
We don't know the sample mean or the sample size (number of bottles), so we'll use the worst-case scenario to find the sample size that gives the largest margin of error.
The worst-case scenario is when the sample mean is equal to the population mean (μ) plus the margin of error (0.1 ounces), and the sample size is as small as possible (which gives the largest margin of error).
So, we have:
0.1 = 1.645 x (0.5/sqrt(n))
Solving for n, we get:
n = (1.645 x 0.5/0.1)²
n = 68.225
Rounding up to the nearest whole number, we get:
n = 69
Therefore,
We need to sample at least 69 bottles to construct a 90% confidence interval for the mean volume of the wine bottles with a margin of error at most 0.1 ounces.
Learn more about confidence intervals here:
https://brainly.com/question/17212516
#SPJ1
