Suppose that 30% of all students who must buy a textbook for a particular course

Question

Suppose that 30% of all students who must buy a textbook for a particular coursewant a new copy whereas the other 70% want a used copy. Consider randomly selecting

20 students.

a. What are the mean and standard deviation of those who want a new copy of the book?

b. What is the probability that the number of students who want new a copy iswithin two standard deviations from the mean value? Use Table A.1.

c. Suppose that new copies are sold for $100 and $70 for used.  What is the expectedvalue of total revenue from the sale of the 20 copies purchased? [Hint: Let (X)= the revenue when  of the 20 students want new copies. Express this as a linearfunction of X.]

Explanation / Answer

a) What are the mean value and standard deviation of the number who want a new copy
of the book?

mean = np = (20)0.30 = 6.000

std dev = sqrt(npq) = sqrt(20*.3*.7) = 2.049



b) What is the probability that the number who want new copies is more than two standard
deviations away from the mean value?

P(X < 1.9) OR P(X > 10.1)

Since this is Binomial, use the Binomial formula ...

P(X < 1.9) = P(0) + P(1) = 0.0076
P(X > 10.1) = P(11) + ... + P(20) = 0.0171

P(X < 1.9) + P(X > 10.1) = 0.0076 + 0.0171 = 0.0247



c) The bookstore has 15 new copies and 15 used copies in stock. If 20 people come in
one-by-one to purchase this text, what is the probability that all 20 will get the type
of book they want from the current stock?

30 books x 30% = 9 want new books and 21 want used books ...

P(X = 9) = 30C9 (0.3^9)(0.7^21) = 0.1573

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