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A Statistics Department Is Contacting Alumni by Telephone Asking for Donations

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A Statistics Department is contacting alumni by telephone asking for donations to help fund a new computer laboratory. Past history shows that 80% of the alumni contacted in this manner will make a contribution of at least $50. A random sample of 20 alumni is selected. Let x represent number of alumni that makes at contribution of at least $50.
What is the probability that exactly 15 alumni will make a contribution of at least $50?
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What is the probability that between 14 and 18 alumni, inclusively, will make a contribution of at least $50?
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What is the probability that less than 17 alumni will make a contribution of at least $50?
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What is the probability that more than 15 alumni will make a contribution of at least $50?
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How many alumni would you expect to make a contribution of at least $50?
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Definitions:

Discretion

The power or right to make decisions based on one's own judgment rather than following a strict rule or protocol.

Rules Of Agency

Guidelines governing the relationship between a principal and an agent, where the agent acts on behalf of the principal.

Officers

Officers are individuals charged with the management and operational duties within an organization, often holding specific titles and responsibilities.

Corporate Articles

Legal documents filed with a governmental body to formally establish the existence of a corporation under the law.

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