brooklyn4932
10.06.2020 •
Mathematics
Please help me, I need help badly
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Ответ:
a) represent the mean
represent the sample standard deviation
b)
Step-by-step explanation:
Previous concepts
The margin of error is the range of values below and above the sample statistic in a confidence interval.
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
Solution to the problem
Assuming the X follows a normal distribution
From the central limit theorem the distribution for the sample mean is given by:
Data given: 7, 1, 6, 3, 6, 7
Part a
We can calculate the sample mean and deviation with the following formulas:
represent the mean
represent the sample standard deviation
Part b
From the central limit theorem we know that the standard error is given by:
And the estimation for the standard error is given by:
And replacing the values we got: