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Binomial Probability Problems 1) Records of a health insurance company show that 30% of its policyholders over 50 submit a claim during the year. 15 policyholders over 50 are selected at random; what is the probability that at least 10 will submit a claim during the year? What is the probability that 4 will submit a claim during the year? How many do you expect to submit a claim. What is the standard deviation? 2) Plastic is now surpassing aluminum as the packaging material of choice for soft drinks. According to a recent article, 80% of all new vending business is going to plastic. If a random sample of 10 new vending businesses is selected, what are P(X>2), P(X