Question

4.2) Recent census data supports the case that life expectancy is correlated with one's income bracket. Given a small town with a population of 13446 Individuals has a distribution of life expectancy loosely based on the recent census, determine the following probabilities with fourth decimal accuracy. 75-76 Row Sum 583 123 Expectancy in years Rich Upper Middle Class Middle Class Class Lower Middle Class Poor Column Sum Life Expectancy at Income Class: 89-95 86-88 81-8577-80 226 175 123 601 1461 495 271 665 1287 2183 206 464 2055 37 57 114 207 1735 3444 3566 3434 632 2951 5206 4008 698 13446 283 1267 Use the following event variable declarations within probability notation to find the associated probabilities with fourth decimal accuracy. A Event that an individual of the town has a life expectancy of 89-95 years. B-Event that an individual of the town has a life expectancy of 86-88 years. C=Event that an individual of the town has a life expectancy of 81-85 years D-Event that an individual of the town has a life expectancy of 77-80 years E-Event that an individual of the town has a life expectancy of 75-76 years. R=Event that an individual of the town is rich S Event that an individual of the town is of the upper middle class. M-Event that an individual of the town is of the middle class. L Event that an individual of the town is of the lower middle class F Event that an individual of the town is poor Note that due to restrictions in the pull down menus used below that the intersection of two events will be indicated with a lower case "n". This means that P(B L ) = P(B n L). 4.2A) Find the probability of drawing an individual from the town that has a life expectancy of 86-88 years P(B) 4.2b) Find the probability of drawing an individual from the town that has a life expectancy of 86-88 years and is poor: P( BF) 4.2c) Find the probability of drawing an individual from the town that is rich and is of the lower middle class PIR )

Answer 1

a) P(B) = 3444/13446 = 0.2561

b) P(B n F) = 57/13446 = 0.0042

c) P(R n L) = 0    (they are disjoint event)

d) P(R U L) = (583 + 4008)/13446 = 0.3414

e) P(F U E) = P(F) + P(E) - P(F and E) = 698/13446 + 1267/13446 - 283/13446 = 0.1251