Question

3. In general, the weights of adult male siberian tigers is normally distributed with a mean of 380 pounds and a standard deviation of 15 pounds.

(a) Based on those values, what is the probability that a random tiger would weigh less than 370 pounds?

(b) Now suppose that the following list contains the weight in pounds of ten randomly selected adult male siberian tigers. (389, 392, 385, 394, 388, 379, 392, 390, 388, 382) What is the sample mean and sample standard deviation?

(c) If the theoretical values were correct, what would be the expected value of the sample mean? What would be the expected variance?

(d) Based on this sample information, create a 95% confidence interval for the mean weight.

(e) Show that, in general, the sample mean is an unbiased estimator for the population mean.

Answer 1