In textbooks published by a certain publisher, the number of typographical error

Question

In textbooks published by a certain publisher, the number of typographical errors (typos) and the corresponding percent frequency are given in the table below. Number of typos Percent frequency 20 32 25 16 Find the mean and variance of the number of typos in a textbook published by this publisher a. b. Suppose that 10 textbooks from this publisher are chosen at random. Find the probability that 6 of these texts contain at most one typo and the remaining 4contain more than one typo. Suppose that 10 textbook titles from this publisher are chosen at random. Find the mean and variance of the number of texts that contain at most one typo. c.

Explanation / Answer

a)

Mean = 161/100 = 1.61 (xbar)

std. dev. = sqrt(22.2526/100) = 0.4717

b)

Probability of at most one typo = 0.52 (20 + 32)

Required probability = 10C6*0.52^6 * 0.48^4 = 0.22

c)

here p = 0.52 and n = 10

mean = np = 0.52 * 10 = 5.2

std. dev. = sqrt(npq) = sqrt(10 * 0.52 * 0.48) = 1.58

Number of typos(xi) Percent Frequency(p) xi*pi (xi-xbar)^2 0 20 0 2.5921 1 32 32 0.3721 2 25 50 0.1521 3 16 48 1.9321 4 4 16 5.7121 5 3 15 11.4921 Total 161 22.2526

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