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6.4 Normal Approximations To Binomial Distributions Recall what a Binomial Distribution is Features of a binomial experiment 1. 2. 3. 4. There are a fixed number of trials, n. The n trials are independent and repeated under identical conditions Each trial only has two outcomes: Success “S” and Failure “F” Fore each individual trial the probability for success, p, is the same. The probability of failure, q, is 1-­‐p. 5. The central problem is probability of r successes out of n trials. Mean and Standard Deviation of the Binomial distribution µ = np is the mean or EXPECTED NUMBER OF SUCCESSES σ = npq that is the standard deviation of number of successes *******Normal probabilities can only be used IF__________________________________________ Notice the graphs Do you try to pad an insurance claim to practice your deductible? About 40% of all americans try to pad their insurance claims. You work for an insurance company that just received 128 insurance claims. What is the probability that half or more have been padded? From 40 to 64 of the claims have been padded?