3.21 In textbooks published by a certain publisherthe number of typographical er

Question

3.21 In textbooks published by a certain publisherthe 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 . a. Find the mean and variance of the number of typos in a textbook published by this publisher 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 4 contain more than one typo. C. 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.

Explanation / Answer

a)

mean =1.61

variance =1.5579

b)

probabaility of at most one typo =0.52

and probability of more then onre typo =0.48

therefore probability of 6 for at most one typo and 4 for more then one typo =(0.52)6*(0.48)4 =0.00105

c)

probability of at most one typo p=0.52

therefore mean =np =10*0.52=5.2

and variance =np(1-p) =10*0.52*(1-0.52) =2.496

x p(x) xP(x) x2P(X) (x-)2 (x-)2P(x) 0 0.2000 0.000 0.000 2.592 0.518 1 0.3200 0.320 0.320 0.372 0.119 2 0.2500 0.500 1.000 0.152 0.038 3 0.1600 0.480 1.440 1.932 0.309 4 0.0400 0.160 0.640 5.712 0.228 5 0.0300 0.150 0.750 11.492 0.345 total 1 = 1.61 4.150 22.253 2= 1.5579 std deviation=     =    2 = 1.2482

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