Solve the following word problems for the unknown. Round decimals to hundredths and p ercents to the nearest tenth when necessary. A letter carrier can deliver mail to 112 homes per hour by walking and 168 homes per hour by driving. a. By what percent is productivity increased by driving?b. If a new ZIP Code system improves driving productivity by 12.5%, what is the new number of homes per hour for driving?
ST 701 Week Four Notes MaLyn Lawhorn September 5, 2017 and September 7, 2017 Independence In words, events A and B are said to be independent if knowledge that B occurred doesn’t change our uncertainty about A. Mathematically, this can be written as if P(B) > 0, then A and B are independent events if P(AjB) = P(A). However, this deﬁnition makes it appear as if direction matters. It sounds as if A being independent from B is not the same as B being independent from A, but this is not the case. A more formal, but less intuitive, mathematical deﬁnition of independence is if A and B are in- dependent events, P(A [ B) = P(A)P(B). In many problems, we can associate the word inde- pendence with the action of multiplying probabilities because of this deﬁnition. The notation for independence is AB. Although the two mathematical deﬁnition of independence seem different, they are actually ”equiv- alent,” because fromP(A\B)n ﬁnd the more intuitive deﬁnition from the more formal one as follows. Recall that P(AjB) = P(B) . P(A \ B) P(AjB) = P(B) P(A)P(B) = P(B) = P(A): There are several types of questions that can be asked regarding independence. ▯ Use the fact that independence must hold from context of the problem to simplify some probability calculations ▯ Examples: – Explain why when tossi