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August 17, 2024

Calculations

31. Instructions: Show your complete solution. Simply giving the final answer without showing your calculations will NOT merit any points. If you’re using PhStat or Excel calculations, upload the excel file. You can also take a screenshot of your calculations by hand, and upload it here.

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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