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 is within two standard deviations from the mean value?

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

Explanation / Answer

p = 0.30 , n = 20 , q = 1 -p = 1 -0.30 = 0.70

a) mean = n * p = 20 * 0.30 = 6

std.deviation = sqrt(npq) = sqrt ( 20 * 0.30 * 0.70) = 2.049

b) By empiriacal rule,

mean - 2 * Std.deviation and mean + 2 * Std.deviation

= 6 - 2 * 2.049 and 6 + 2* 2.049

= 1.902 and 10.098

P(1.902 < X < 10.098)

BY central limit theorem,

z = ( x - mean) / s

z = P( ( 1.902 - 6) / 2.049 < z < (10.098 - 6 ) / 2.049)

= P( -2 < z < 2)

P(1.902 < X < 10.098) = P( -2 < z < 2) = 0.9545

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