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A workshop makes tables. The cutting and sanding operations are independent. Based on historical data, under...

A workshop makes tables. The cutting and sanding operations are independent. Based on historical data, under normal conditions, 1% of cut wood for the tables, and 2% of sanded wood for the tables are defective.

Assume that one table is randomly selected from a lot of cut and sanded tables.

a. What is the probability that at least one of the operations (cutting and sanding) will be defective?

b. What is the probability that in a production lot of 10 tables, none of the tables is defective?

c. What is the expected number of defective tables in a production lot of 15 tables? What is the standard deviation?

math   Statistics-And-Probability   
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Answer #1

(a). Probability that atleast one of the operatins will be defective = (0.01*0.02 + 0.01*0.98 + 0.99*0.02) = 0.0298

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(b). probability that none of the 10 tables is defective = (1-0.0298)10 = 0.7389

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(c). Expected number of defective tables in production lot of 15 tabes = 0.9702 * 0 + 0.0298 * 15 = 0.447

Expected number of tables to be defective in a lot of 15 tables is 0 (due to very high probability of not defective which is 0.9702)

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