Sample items are popular in supermarkets Costumer take free

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?

Solution

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%