Question

Suppose that 30% of all students who have to buy a textbook for Statistics want a new copy (the successes!), while the rest 70% want a used copy. Consider randomly selecting 15 buyers. (a) Find the mean and standard deviation for the number who want to buy a new copy of the book Mean = 15*.3 Standard deviation = sqrt(15*.3*.7) (b) Is that probability that the number of buyers who want new copies is more than two standard deviations away from the mean value? Probability= 1-.984757474+.004747562 (c) The bookstore has 13 new copies and 13 used copies in stock. If 15 people come in one by one to buy this textbook, what is the probability that all 15 will get the type of book they want from current stock? Probability= .999999483-.0352676 Hint: Consider X: the number of buyers who want a new copy. For what values of X will all 15 buyers get what they want? (d) Suppose that new copies cost $134 and used copies cost $67. Assume that the bookstore has currently 15 new copies and 15 used copies. What is the expected total revenue from the sale of the next 15 copies? Expected Revenue=

Answer 1

Explanation:

a.

mean = E(X)

= no = 15 x 0.3

= 4.5

Standard deviation

= √np(1-p)

= √15x0.3x0.7

= √3.15

= 1.775

B.

Probability of number of buyers who want new copy

P(x>mean+2sd)

= P(x>4.5+2(1.775))

P(x>8.05)

= 1-(0.984757474+0.004747562)

= 0.01049

= 0.0105

C.

Σ13 (15Cx) x (0.3^x)(0.7)^15-x

= 0.9647

D. (4.5*237)+(15-4.5)*67

= 616.5+703.5

= $1320

Expected revenue from sale of next 15 copies is $1320