Sample items are popular in supermarkets. Costumer take free samples in about 60

Question

Sample items are popular in supermarkets. Costumer take free samples in about 60% of the cases. When 317 costumers are observed, what is the probability that more than 180 will take a sample? Do you try to pad an insurance claim to cover your deductible? About 40% of all U.S. adults will try to pad their insurance claim this year. A director of an insurance adjustment office has just received 128 insurance claims to be processed. What is the probability that more than 80 of the claims are not padded?

Explanation / Answer

Normal Distribution
Mean ( np ) =190.2
Standard Deviation ( npq )= 317*0.6*0.4 = 8.7224
Normal Distribution = Z= X- u / sd                   
a)
P(X > 180) = (180-190.2)/8.7224
= -10.2/8.7224 = -1.1694
= P ( Z >-1.169) From Standard Normal Table
= 0.8790
b)
Normal Distribution
Mean ( np ) = 128 * 0.60 = 76.8
Standard Deviation ( npq )= 128*0.6*0.4 = 5.5426
Normal Distribution = Z= X- u / sd                   
P(X > 80) = (80-76.8)/5.5426
= 3.2/5.5426 = 0.5773
= P ( Z >0.577) From Standard Normal Table
= 0.2819 ~ 28.19%

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