7) You apply for 14 jobs. Each application has a 40#% chance of leading to an interview. Every interview has a 60%% chance of leading to a job offer. Hint: keep your head straight about which P(success) applies to which part and it will be easy! What is the chance that an application leads to a job offer? bj what is the expected number of interviews? c) What is the expected number of job offers? d) what is the chance you get exactly 3 job offers? What is the chance you get exactly 7 interviews? What is the chance you get exactly 3 job offers if you get 6 interviews? Assume you build a Candy castle for which you buy a bag of gummy bears, a block of chocolate and a bag of nuts. The weight of the three ingredients is a random variable (X X and X ] with mean weights Hi = 200 gram, : = 400 gram and u = 150 gram. The bags and blocks are not measured top perfection so the standard deviation of the three is of = 10, o, = 9 and of = 15. Find the expected weight and variance for the weight of the candy castle assuming that you use up all the ingredients without weight loss! Assume you enter Berea with the expectation to work all 4 summers (including the one after you graduate). The following table gives you the number of hours you plan to work, the expected wage rate per hour (W) and the variance of the wage rate. How much do you expect to earn over the 4 summers and what is the variance and standard deviation of you total 4-summer income? Year Hours E(W) Freshman 100 $7 1 Sophomore 200 $9 1.5 Junior 300 513 2 Senior 200 $15 How much is your expected income over the 4 summers What is the variance and standard deviation of you total 4-summer income? Berea taxes students' income at 40%. What is the expected income and variance of our net income over the next 4 summers? (assume you have to pay no other taxes) 10) You get three x-mas presents from your aunts. You never know exactly how much money they will give you, but you know that Aunt Annie gives you on average $30 with a variance of 100, Aunt Becky gives you on average $50 with variance 200 and Aunt Celine gives you on average $100 with variance 400. Assuming independence, What is the expected amount of money you will get from your aunts for x-mas? bl What is the variance of the amount of money you expect to get for x-mas from your aunts? 11) Bonus points! 3 points for the first student, 2 for the second and 1 for the third who gets the correct solution to me (email me the spread sheet and explain how you did it) Assume that snowflakes come in 40,000 basic types, with each of the 40,000 types comprising the same proportion of an infinite total population of snowflakes. If we randomly sample 100 snowflakes, what is the probability that at least two will be duplicates of each other