Answer to Question #346677 in Statistics and Probability for lay

Question #346677

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


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Expert's answer
2022-06-01T11:40:46-0400
SE=σn=σ2nSE=\dfrac{\sigma}{\sqrt{n}}=\dfrac{\sqrt{\sigma^2}}{\sqrt{n}}n=σ2(SE)2=121592=15n=\dfrac{\sigma^2}{(SE)^2}=\dfrac{1215}{9^2}=15




Var(Xˉ)=σ2n=(9)2=81Var(\bar{X})=\dfrac{\sigma^2}{n}=(9)^2=81


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