Calculations
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This is a binomial distribution problem.
According to the Center for Client Retention, 30% of callers to automated customer-service systems will automatically opt to go to a live operator when given the chance.
Consider a random and independent sample of 20 callers who contact an automated customer service system, what is the probability that:
1. At least 5 but not more than 12 opt NOT to talk to a live operator?
2. Less than 7 or more than 11 opt to talk to a live operator?
3. Fewer than 4 opt NOT to talk to a live operator?
4. Exactly one will automatically opt to talk to a live operator?
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