Question

The average salary for a certain profession is ​60000$. Assume that the standard deviation of such salaries is ​36,000$. Consider a random sample of 66 people in this profession and let x represent the mean salary for the sample.

1) What is μ x¯​?
2) What is ​σ x¯? ​(Round to 2 decimal places as​ needed.)

Answer 1

The population mean of the salaries for the profession is $60,000 and the sample mean of a random sample of 66 people will also be $60,000. The standard deviation of the sample mean is approximately $4,424.72.

Step-by-step explanation:

1) The population mean of the salaries for the certain profession is $60,000, represented as μ. The sample mean of a random sample of 66 people, x¯, will also be $60,000 since the sample mean is an unbiased estimator of the population mean.

2) The standard deviation of the sample mean, σ x¯, can be found by dividing the standard deviation of the population by the square root of the sample size. In this case, σ x¯ = 36,000 / √66 ≈ 4,424.72.