Question 2 (a) After having some lunch in KFC, you drive to IKEA for buying some bowls, however you lost your keys either in the KFC or in IKEA. The probability for loosing it at either location is...

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Extracted text: Question 2 (a) After having some lunch in KFC, you drive to IKEA for buying some bowls, however you lost your keys either in the KFC or in IKEA. The probability for loosing it at either location is 1/2. The probability that you will find your keys if you lost it in IKEA is 30%, while the probability that you will find it if you lost it at the KFC is 70%. i) Please specify the probability that you will not find your keys in the KFC? Define all the events carefully needed in the calculation. ii) You went to KFC but you could not find your keys there. Given this information, what is the probability that you will find it in IKEA? (b) Last century, the annual income of farmers in a country are normally dis- tributed with mean of 500$ and standard deviation of 200$. i) Calculate the probability that a randomly selected farmer's income is between 500$ and 520$. ii) If the probability that the annual income of farmers in this county is within (500-a , 500+a) is not less than 0.95, how much at least o is? iii) Calculate the probability that the sum of 25 randomly selected farmers' income will be more than 13,500$.