Question

Note: - Include all work and clearly designate your answer. Credit will be based on the merit of the work provided Round probabilities to 3 decimal places. -Each question is worth 20 points. 1. A company manufactures steel tubes. Each tube is tested for two attributes: internal diameter and surface finish. 150 such tubes are randomly selected and inspected. Results are provided on following table. Surface Finish Pass No pass Total Too small Too large Within Specifications 12 15 90 16 37 97 Internal Diameter 7 150 a. A tube is "acceptable" only if it passes the Surface Finish test and its internal diameter is within specifications. What is the probability that a randomly selected tube is "acceptable? b. Given that a tube's internal diameter is "Too large", what is the probability that it does not pass t surface finish test? c. If a tube's internal diameter is "Too Small", the tube is re-workable. What percentage of unacceptable tubes are re-workable?

Answer 1

a.

Probability that a randomly selected tube is acceptable

=P(tube passes surface finish test and internal diameter is within specifications)

= Number of tubes passes surface finish test and internal diameter is within specifications / Total tubes

Probability that a randomly selected tube is acceptable = 90 / 150 = 0.6

b.

P(tube does not pass surface finish test / internal diameter is too large)

= P(tube does not pass surface finish test and internal diameter is too large) / P(internal diameter is too large)

P(tube does not pass surface finish test and internal diameter is too large) = 22 / 150 = 0.1467

P(internal diameter is too large) = 37 / 150 = 0.2467

P(tube does not pass surface finish test / internal diameter is too large) = 0.1467 / 0.2467 = 0.595

c.

Probability that a randomly selected tube is acceptable = 0.6

Probability that a randomly selected tube is unacceptable = 1 - 0.6 = 0.4

P(Tube is re-workable ) = P(tube's internal diameter is too small) = 16 / 150 = 0.1067

Percentage of unacceptable tubes that are re-workable = (0.1067 / 0.4)*100 % = 0.2667*100 % = 26.67 %