Suppose that 30% of all students who have to buy a text for a particular course

Question

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% want a used copy. Consider randomly selecting 25 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 value? (Round your answer to three decimal places.) (c) The bookstore has 15 new copies and 15 used copies in stock. If 25 people come in one by one to purchase this text, what is the probability that all 25 will get the type of book they want from current stock? Hint: Let ? the number who want a new copy. For what values of X wi all 25 get what they want ind your answer tot reede nmal places. (d) Suppose that new copies cost $100 and used copies cost $70. Assume the bookstore currently has 50 new copies and 50 used copies. What is the expected value of total revenue from the sale of the next 25 copies purchased? [Hint: Let h(x)the revenue when X of the 25 purchasers want new copies. Express this as a linear function.] Indicate what rule of expected value you are using O E(aX + b)-a-E(X). E(aX + b) a-E(X) + b

Explanation / Answer

Answer :

(a). p = 0.30, q= 1-p = 0.70

n = 25

Mean = 25*0.30 = 7.5

Standard deviation = ?(25*0.3*0.7) = 5.25

(b) . Probability that number who wanted new copies lies 2 standard deviation away from mean = 1- probability of lying in 2 standard deviation = 1-0.95 = 0.05, (using standard normal distribution).

(C). For X <= 15 all the customers gets what they want. So probably of everybody getting what they want = probability (X<= 15). Z value corresponding to this =( 15 - 7.5)/5.25 = 1.42

So probability = p(z<=1.42) = 0.9222

(D).E(ax+b) = aE(x)+b , linearity theorem.

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