Answer:
This sampling distribution will only reflect the nature of its population distribution (strongly skewed right because the sample size of each sample, 9, is way less than the sample size of 30 required for the sampling distribution to be approximately normal) with mean 404 inches and standarddeviation of sampling distribution equal to 43 inches.
Step-by-step explanation:
The Central limit theorem explains that for an independent, any random set of sample taken from such a population distribution will have a distribution that is approximately normal (provided that the sample size is large enough) with the mean of sampling distribution also approximately equal to the population mean and the standard deviation of the sampling distribution is given as
σₓ = (σ/√n)
where
σ = population standard deviation
n = sample size
To work these out,
Mean of sampling distribution = population mean
μₓ = μ = 404 inches
Standard deviation of the sampling distribution = σₓ = (σ/√n)
σ = population standard deviation = 129 inches
n = sample size = 9
σₓ = (129/√9) = 43 inches.
For most databases, the 'large enough' criteria for the sampling distribution to be approximately normal is a sample size of about 30 and it gets closer as the sample size becomes larger.
The sample size in the question is 9 which is way less than 30, hence, this sampling distribution will only reflect the nature of its population distribution (strongly skewed right) with mean 404 inches and standarddeviation of sampling distribution equal to 43 inches.
Hope this Helps!!!
