Answer to Question #346677 in Statistics and Probability for lay

Question

Based on a study, the average typing speed of women is normally distributed. Karen verified the results by conducting a similar study and found out that the standard error of the sample mean is 9 words per minute using a sample with a variance of 1 215. Determine the variance of the sampling distribution

Answer 1

$$SE=\dfrac{\sigma}{\sqrt{n}}=\dfrac{\sqrt{\sigma^2}}{\sqrt{n}}$$ $$n=\dfrac{\sigma^2}{(SE)^2}=\dfrac{1215}{9^2}=15$$

$$Var(\bar{X})=\dfrac{\sigma^2}{n}=(9)^2=81$$