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STAT 353 Homework 3 STAT 353: Homework 3 (Probability Distributions) Points Possible: 10 Problems: . A synthetic fabric is produced in continuous rolls of uniform width. The probability distribution of the number of imperfections per 10 meters is given in the table. 0 # imperfections probability 4 0.41 0.37 0.16 0.05 0.01 a) b) What is the expected number of imperfections in a 10 meter section? Find the standard deviation in the number of imperfections per 10 meter section.

please do this probability problem and make sure you explain it .
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# imperfection(X) | P(X) | X*P(X) | X2+p(X) 0.41 0.37 0.16 0.32 0.05 0.01 0 0 0.37 0 0.37 0.64 0.45 0.16 1.62 2 4 Total 0.15 0.04 0.88 a)Expected number ofimperfection in a 10 meter section is E(X)-Σ X * P(X) 0.88 b) The standard deviation in the number ofimperfectionper 10 meter section is SD(X)-E(X)- (E(X))2 Now, E(X2)-XX2P(X)-1.62 SD(X)-V1.62-(0.88)2-V1.62-0.7744-v0.8456-091 9565

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