Question

A retail company must choose a few employees to send to a national retail conference. Of the 746 employees at this company, 470 are male.
1) If 5 employees are randomly chosen, find the probability that exactly 4 are male.

ABC Manufacturing has a policy that it will reject a shipment of parts from its supplier if inspectors find any defective parts in a random sample of 6 parts from the shipment. The supplier has been in business many years and has a long-term defective rate for parts of 8.9%.
2) What is the probability that a shipment will be rejected after a given sample of parts is checked?   

Suppose you wanted to evaluate the performance of the three judges in Smallville, Texas: Judge Adams, Judge Brown, and Judge Carter. Over a three-year period in Smallville, Judge Adams saw 23% of the cases, Judge Brown saw 30% of the cases, and Judge Carter saw the remainder of the cases. 4% of Judge Adams’ cases were appealed, 6% of Judge Brown’s cases were appealed, and 8% of Judge Carter’s cases were appealed.

3) Given a case from this three-year period was not appealed, what is the probability the judge in the case was not Judge Brown?

Answer 1

1)

here as sample size n= 5 and N =total populaton size =746

as n/N <=0.05 ; threfore we can use binomial approximation

here probability of male =(470/746)=0.63

threfore P(exactly 4 are male)= =0.2914

2)

P( shipment will be rejected)=1-P(all parts are defect free)=1-(1-0.089)⁶ =0.4284

3)P(case was not appealed)=P(Judge Adams and case was not appealed)+P(Judge Brown and case was not appealed)+P(Judge Carter and case was not appealed)

=0.23*(1-0.04)+0.3*(1-0.06)+(1-0.23-0.3)*(1-0.08)=0.9352

hence P(not Judge Brown|case was not appealed)=1-P(Judge Brown|case was not appealed)

=1-0.3*(1-0.06)/0.9352=0.69846