Suppose that the sampling distribution of size 10 has a mean of 30 and standard deviation of 3. Calculate 1. μ 2. o =

Use the central limit theorem to find the mean and standard error of the mean of the indicated sampling distribution. Then sketch a graph of the sampling distribution. The per capita consumption of red meat by people in a country in a recent year was normally​ distributed, with a mean of 106 pounds and a standard deviation of 38.6 pounds. Random samples of size 17 are drawn from this population and the mean of each sample is determined.   Ux = Standard deviation =

A sample consists of n=6 scores: 2,7,4,6,4,7 1. Compute the mean and standard deviation for the sample 2. Find the Z score for each score in the sample. 3. Transform the original sample into a new sample with mean of M=50 and s = 10

Suppose that the sampling distribution of size 10 has a mean of 30 and standard deviation of 3. Calculate  σ = (Round to two decimal places)

Assume that a sample is used to estimate a population mean µ. Find the margin of error M.E, that corresponds to a sample of size 11 with a mean of 65.6 and a standard deviation of 5.6 at a confidence level of 95%.

An ecologist is studying the impact of local polluted waters on the growth of alligators. The length of adult male alligators typically follows a normal distribution with a standard deviation of 2 feet. The ecologist wants to estimate the mean length of this population of alligators. Suppose she samples n alligators at random and uses the sample mean, X to as an estimator for u. a. What is the bias and variance of the estimator? (Note, these may be a function of n.) b. If n = 4, what is the probability that the estimator is within one foot of the true mean? (I.e. find P(|X – µ| < 1). c. What sample size, n, is required for the estimator to be within one foot of the true mean with 95% probability? (I.e. find the value of n that satisfies P(|X – µ| < 1) = 0.95.) d. Suppose the ecologist ends up sampling n = 9 alligators and calculates a sample mean of ī = 10.4 feet. Construct a 95% confidence interval for the population mean. e. Give an interpretation for the interval obtained in (d).

8. In the UK (United Kingdom) Baby Birth weight can be approximated by a Normal Distribution with N(3.39, 0.55) with numbers being in kg (kilograms) A. What are the Mean birth weight and Standard Deviation of birth weight. B. What weights are more than 2 Standard Deviations above and below the Mean birth weight. C. Compute the Z-Score for a 4 kg birth.

A random sample of size 36 is taken from a population with mean µ = 17 and standard deviation σ = 6. What are the mean and the standard deviation for the sampling distribution of the sample mean?

Suppose weights of running shoes have an unknown distribution with mean 11 and standard deviation 2 ounces. A sample of size n = 61 is randomly taken from the population and the mean is taken. Using the Central Limit Theorem for Means, what is the standard deviation from the sample mean distribution?

Suppose that random samples of size 36 are repeatedly drawn from a populationwith mean 28 and standard deviation 9. Describe the sampling distribution of X¯. NOTE: Please explain each part, so the problem can be used as a Study Guide