Questions: The heights of fully grown trees of a specific species are normally distributed, with a mean of 54.0 feet and a standard deviation of 5.00 feet. Random samples of size 20 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. The mean of the sampling distribution is μx= . The standard error of the sampling distribution is σx̅= . (Round to two decimal places as needed.)

The heights of fully grown trees of a specific species are normally distributed, with a mean of 54.0 feet and a standard deviation of 5.00 feet. Random samples of size 20 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. The mean of the sampling distribution is μx= . The standard error of the sampling distribution is σx̅= . (Round to two decimal places as needed.)
Transcript text: Save The heights of fully grown trees of a specific species are normally distributed, with a mean of 54.0 feet and a standard deviation of 5.00 feet. Random samples of size 20 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. The mean of the sampling distribution is $\mu_{\mathrm{x}}=$ $\square$ . The standard error of the sampling distribution is $\sigma_{\bar{x}}=$ $\square$ . (Round to two decimal places as needed.)
failed

Solution

failed
failed

Solution Steps

Step 1: Calculate the mean of the sampling distribution

The mean of the sampling distribution is the same as the mean of the population: \[ \mu_{\bar{x}} = \mu = 54.0 \text{ feet} \]

Step 2: Calculate the standard error of the sampling distribution

The standard error of the sampling distribution is given by: \[ \sigma_{\bar{x}} = \frac{\sigma}{\sqrt{n}} \] where \(\sigma = 5.00\) feet and \(n = 20\).

\[ \sigma_{\bar{x}} = \frac{5.00}{\sqrt{20}} \approx 1.1180 \text{ feet} \]

Final Answer

The mean of the sampling distribution is \(\mu_{\bar{x}} = 54.0\) feet.

The standard error of the sampling distribution is \(\sigma_{\bar{x}} = 1.12\) feet.

{"axisType": 3, "coordSystem": {"xmin": 40, "xmax": 70, "ymin": 0, "ymax": 0.05}, "commands": ["y = (1/(1.12_sqrt(2_pi)))_exp(-0.5_((x-54)/1.12)**2)"], "latex_expressions": ["$y = \\frac{1}{1.12\\sqrt{2\\pi}}e^{-0.5\\left(\\frac{x-54}{1.12}\\right)^2}$"]}

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
Complete the problem. (From Example 2) 2. Anwar Mabak incurs 2,818.00 in annual fixed costs to operate his car. He estimates that he will drive 22,500 miles during the year. What are his annual variable costs if his cost per mile is 0.32?
failedAnswered
Write a balanced half-reaction for the reduction of bismuth oxide ion (BiO3-) to bismuth ion (Bi3+) in basic aqueous solution. Be sure to add physical state symbols where appropriate.
failedAnswered
In which of the following aqueous solutions would you expect AgBr to have the lowest solubility? A) 0.15 M KBr B) pure water C) 0.10 M AgNO3 D) 0.10 M LiBr E) 0.20 M NaBr
failedAnswered
What should a nurse teach a client who has been diagnosed with hepatitis A? 1. Hepatitis A is spread through blood and body fluid. 2. Chronic liver disease is a common complication of hepatitis A. 3. Symptoms of hepatitis A include malaise, dark colored urine, and jaundice. 4. Treatment includes alpha-interferon and ribavirin.
failedAnswered
For the given functions, find (f ∘ g)(x) and (g ∘ f)(x) and the domain of each. f(x)=(1-x)/(21x), g(x)=1/(1+21x)