The Central Limit Theorem states that the sampling distribution of the sample means approaches a normal distribution as the sample size gets larger — no matter what the shape of the population distribution. This fact holds especially true for sample sizes over 30.
a) Since random samples of size n = 36 (36>30) are drawn, then "\\bar{X}" has an approximately normal distribution.
"\\sigma_{\\bar{X}}=\\sigma\/\\sqrt{n}=27\/\\sqrt{36}=4.5"
"\\bar{X}\\sim N(60, 4.5^2)"
Then
b)
If "\\bar{X}=69," then
c)
d)
"\\mu_{\\bar{X}}+2\\sigma_{\\bar{X}}=60+2(4.5)=69"
Maximum usual value is "69." Minimum usual value is "51."
It would be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 51.
It would be unusual for a random sample of size 36 from the x distribution to have a sample mean greater than 69.
It would not be unusual for a random sample of size 36 from the x distribution to have a sample mean less than 69.
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Dear Fhely Montefalcon, please use the panel for submitting a new question.
Mean is 83 and sample size is 39
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