SOLUTION: The heights of fully grown trees of a specific species are normally​ distributed, with a mean of 63.0 feet and a standard deviation of 6.25 feet. Random samples of size 16 are dr

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Question 1150900: The heights of fully grown trees of a specific species are normally​ distributed, with a mean of 63.0 feet and a standard deviation of 6.25 feet. Random samples of size 16 are drawn from the population. Use the central limit theorem to find the mean and standard error of the sampling distribution. Then sketch a graph of the sampling distribution.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

mu = population mean = 63.0
sigma = population standard deviation = 6.25
n = sample size = 16

The mean of the sample distribution is equal to mu.
So the mean of the sample distribution is 63.

The standard deviation of the sample distribution, aka standard error, is
SE = standard error
SE = sigma/sqrt(n)
SE = 6.25/sqrt(16)
SE = 6.25/4
SE = 1.5625

The distribution looks like this

The sample distribution is in red compared to the original normal distribution in blue (mu = 63, sigma = 6.25). This is to help see that the sample distribution is much more narrow/skinny. The more narrow the distribution, the taller it gets. This is to ensure the total area under the probability distribution curve is always equal to 1. Think of having a very flat rectangle that isnt tall; then rotating the rectangle so that it is now very tall but also very skinny.

Both distributions have the same center (mu = 63) but different spreads or standard deviations.