Only need help with problem 3.14. Thanks! Each month DINGO Ltd receives a shipme

Question

Only need help with problem 3.14. Thanks!

Each month DINGO Ltd receives a shipment of 100 parts from their supplier which will be checked on delivery for defective parts Historically the average number defective was three The new quality assurance procedure involves randomly selecting a sample of three items (without replacement) for inspection. If more than one of the sample is defective the order is returned. What proportion of shipments might be expected to be returned? UK Pro Ltd manufacture footballs for the Far East market with two different standard footballs, standard and professional As part of the quality assurance process, the manufacturing firm chooses 200 footballs from the manufacturing process and either rejects or accepts the footballs according to specified criteria, with the following results: The probability that the football is accepted, the probability that the football is rejected, the probability that the football rejected given selected standard football, and the probability that the football is accepted given selected professional football.

Explanation / Answer

Following is the completed table:

(a)

Out of 200 footballs 138 are accepted so

P(accepted) = 138 /200 = 0.69

(b)

Out of 200 footballs 62 were rejected so

P(rejected) = 62 /200 = 0.31

(c)

P(standard) = 132 / 200

P(rejected and standard) = 43 /200

So the required probability is

P(rejected | standard) = P(rejected and standard) / P(standard) = 43 / 132 = 0.3258

(d)

P(professional) = 68 / 200

P(accepted and professional) = 49 /200

So the required probability is

P(acceped | professional) = P(accepted and professional) / P(professional) = 49 / 68 = 0.7206

Type Accept Reject Total Standard 89 43 132 Professional 49 19 68 Total 138 62 200

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