Question

The heights of fully grown trees of a specific species are normally distributed, with a mean of 53.5 feet and a standard deviation of 5.00 feet. Random samples of size 13 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 = 0 The standard error of the sampling distribution is o: - (Round to two decimal places as needed) Choose the correct graph of the sampling distribution below. ОА. OB Ос. us 53.5 507 535

Answer 1

As the underlying distribution is normal here, the distritbuion of sampling mean would also be normal here. The mean and standard deviaiton of the sampling distribution here is given as:

$\mu_{\bar X} = \mu = 53.5$

$\sigma_{\bar X} = \frac{\sigma}{\sqrt{n}} = \frac{5}{\sqrt{13}} = 1.39$

The distribution here is therefore given as:

49.33 50.72 52.11 53.5 54.89 56.28 57.67

therefore B is the correct graph here.