A study by Great Southern Home Insurance revealed that none of the stolen goods were recovered by the homeowners in 80 percent of reported thefts: [ 6 marks] a. During a period in which 200 thefts occurred, what is the probability that no stolen goods were recovered in 170 or more of the robberies? b. During a period in which 299 thefts occurred, what is the probability that no stolen goods were recovered in 150 or more robberies?

Solution :

Given :

n = 200, p = 80% = 0.8, q = 1 - p = 0.2

   = 5.6569

a). x = 169.5

∴

     = 1.6794

Therefore, probability that the stolen goods were not recovered in 170 robberies or more is = 0.0465

b). x= 149.5

Therefore the probability that the stolen goods were not recovered in the 150 or in more robberies is = 0.9683

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