Automobiles Arrive at a Vehicle Equipment Inspection Station According to a Poisson

question 9

Essay

Automobiles arrive at a vehicle equipment inspection station according to a Poisson process with rate $\alpha$ = 10 per hour. Suppose that with probability .5 an arriving vehicle will have no equipment violations.
a. What is the probability that exactly ten arrive during the hour and all ten have no violations?
b. For any fixed $y \geq 10$
what is the probability that y arrive during the hour, of which ten have no violations?
c. What is the probability that ten "no-violation" cars arrive during the next hour? [Hint: Sum the probabilities in part (b) from y = 10 to $\infty ,$
]

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Definitions:

Lent And Brown

Refers to scholars who contributed to the Social Cognitive Career Theory, focusing on how personal beliefs and social factors influence career decisions and development.

Decisional Balance Sheet

A tool used in cognitive therapy and decision-making that lists the pros and cons of different choices to help evaluate options objectively.

Positive Consequences

These are favorable outcomes or results that occur as a direct result of a particular action or set of actions.

Negative Consequences

Undesirable outcomes or effects that result from an action or decision.