Answer to Question #108159 in Statistics and Probability for Wong Tsz Ching

Question

In a study of monthly salary distribution of residents in Paris conducted in year 2015, it was found that the salaries had an average of €2200 (EURO) and a standard deviation of €550. Assume that the salaries were normally distributed.
Consider sampling with sample size 64 on the above population. Compute the mean of the
̅ sampling distribution of the mean (

Answer 1

The sampling distribution of the mean from a normal distribution is normally distributed with mean $\mu$ and standard deviation $\frac{\sigma}{\sqrt{n}}$ . Thus mean of the sampling distribution of the mean is €2200 and standard deviation is $\frac{€550}{\sqrt{64}}=€68.75$ . Thus the sampling distribution of the mean is N(€2200,€68.75).