(4) Solve the following problems about CLT (Central Limit Theorem). You should be aware of the fact that CLT is not always applicable. (a) [2pts] A state has millions of households. The average annual income of the households is 100,000 dollars and the SD is 40,000 dollars. Fill in the blank with a number: \"There is about a 95% chance that the average annual income of a simple random sample of 1,600 families drawn from is state is more than dollars.\" (You may use the result of the problem 5' in this homework.) (b) Suppose the lengths of phone calls to the receptionist of a small company are i.i.d. with a mean of 5 minutes and an SD of 5 minutes. Let X1, X2, - -- ,Xn be the length of n calls in minutes, and let An = $22121 X,- be the sample average length. In each of the following parts, either nd the chance exactly, or approximate it, or bound it. Do the best you can with the information given. (1) [1m] IP(|A4 5| 3 5) (ii) [2pts] MUAIOW 5| > 0.098). (Use the fact that (M196) =. 97.5%.)