PassageBased on the above data, answer the given subquestions. Let X1,X2,…,X20∼i.i.d. Uniform[8,12]X_1,X_2,\ldots,X_{20}\sim \text{i.i.d. Uniform}[8,12].
QuestionUsing Chebyshev's inequality, find an upper bound for P(∣Xˉ−10∣>2)P(|\bar{X}-10|>2), where Xˉ=(X1+X2+⋯+X20)/20\bar{X}=(X_1+X_2+\cdots+X_{20})/20 is the sample mean. Enter the answer correct to 3 decimal places.