From the central limit theorem, the interval can the researcher be 95% certain that the sample mean will fall within A. $257.82 and $272.18.
How to use the Central limit theorem?
We are given;
Population Mean; μ = $265
Population standard deviation; σ = $40.93
Sample size; n = 130
The central limit theorem (CLT) postulates that the distribution of sample mean approximates a normal distribution with larger sample sizes, disregarding the population's distribution.
This implies that sample sizes equal to or greater than 30 are often considered sufficient for the Central limit theorem to hold.
Thus, by the central limit theorem, the interval can the researcher be 95% certain that the sample mean will fall within A. $257.82 and $272.18.
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