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 8 minutes.
Let 1,2,…, be the lengths of calls in minutes, and let
= 1/ [lim(=1→)] ∑ ,
be the sample average length. In each of the following parts, either find the chance exactly, or approximate it, or bound it. Do the best you can with the information given.
a) P(|₁₆ − 5|<4)
b) P(|₁₆₀₀ − 5|<0.4)