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Sagot :
Using the Central Limit Theorem, the sampling distribution of the sample mean wait time for random samples of size 84 has mean of 11.4 minutes and standard deviation of 0.28 minutes.
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
In this problem, the population has:
- Mean of 11.4 minutes, thus [tex]\mu = 11.4[/tex].
- Standard deviation of 2.6 minutes, thus [tex]\sigma = 2.6[/tex]
Samples of 84 are taken, thus, by the Central Limit Theorem:
[tex]n = 84, s = \frac{2.6}{\sqrt{84}} = 0.28[/tex]
The sampling distribution of the sample mean wait time for random samples of size 84 has mean of 11.4 minutes and standard deviation of 0.28 minutes.
A similar problem is given at https://brainly.com/question/16364846
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