Question

[-/21 Points) DETAILS DEVORESTATO 3.6.052.NVA Suppose that 30% of all students who have to buy a text for a particular course want a new copy (the successes!), whereas the other 70% water.com 15 purchasers (a) What are the mean value and standard deviation of the number who want a new copy of the book? (Round your standard deviation to two decimal places) mean students standard deviation students (b) What is the probability that the number who want new copies is more than two standard deviations away from the mean we? (Round your answer to three decalces) (c) The bookstore has 10 new coples and 10 used copies in stock. If 15 people come in one by one to purchase this text, what is the probability that all 15 will get the type of book they want from current stock? (Hint: Let X - the number who want a new copy. For what values of X will all 15 get what they want Round your answer to three decade (d) Suppose that new copies cost $140 and used copies cost $80. Assume the bookstore currently has 50 new coples and 50 sed copies. What is the expected value of total ree from the sale of the next 15 copies purchased? (Hint: Let h(x) - the revenue when X of the 15 purchasers want new Express this as a linear function $ Indicate what rule of expected value you are using. E(aX+b) - E(X) + b EaX+b) = a E(X). EaX+b) = 32. E(X) EſaX+b) = E(X) + b.

Answer 1

15 k=9 a) mean = = 15 * 0.3 = 4.5, sd = 15 * 0.3* 0.7 = 1.78 6) P(X > 4.5+2*1.78 = 8.06) = P(X > 8) = P(X 2 9) = 15C40.360.715–k = 0.01524 c) X : no.of ppl who want new copies, note all 15 will get what they want if and only if 5 < X < 10, so P(all will get what they want) = P(5< X < 10) = 1500.350.715-k = 0.484 d) h(X) = 140X + (15 – X) * 80 = 60X + 1200, so E(h(X)) = 60E(X) + 1200 = 1470 correct rule EaX + b) = aE(X) + b, so 1st choice. 10 k=5