A population has parameters µ 140.6 and o = 27. You intend to draw a random sample of size n= 186. What is the mean of the distribution of sample means? What is the standard deviation of the distribution of sample means? (Report answer accurate to 2 decimal places.)

Samples of size 14 are selected from a manufacturing process. The mean of the sample ranges is 0.5. What is the estimate of the standard deviation of the population? (Round your answer to 3 decimal places.)

For men heights are normally distributed with a mean of 69 inches and a standard deviation of 2.8 inches. If samples of 25 men are selected at random from the population, would the average height found for each sample be more or less varied than the individual measurements taken for each man?B

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).