for an outdoor concert by the city orchestra, concert organizers estimate that 17,000 people will attend if it is not raining. if it is raining, concert organizers estimate that 6000 people will attend. on the day of the concert, meteorologists predict a 90% chance of rain. determine the expected number of people who will attend this concert.

it is expected that people will attend the concert.

Question

for an outdoor concert by the city orchestra, concert organizers estimate that 17,000 people will attend if it is not raining. if it is raining, concert organizers estimate that 6000 people will attend. on the day of the concert, meteorologists predict a 90% chance of rain. determine the expected number of people who will attend this concert.

it is expected that people will attend the concert.

it is expected that   people will attend the concert.

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "blank_filling_formatter", "explain_then_answer", "tutor", "mastery_adaptive_brevity" ], "needs_drawing": false, "concepts_used": [ "Complementary Events", "Expected Value" ], "new_concepts": [], "current_concepts": [ "Complementary Events", "Expected Value" ] } ## Calculate probability of no rain Using the *Complementary Events* knowledge point $$ \begin{aligned} P(\text{No Rain}) &= 1 - P(\text{Rain}) \ &= 1 - 0.90 \ &= 0.10 \end{aligned} $$ ## Calculate expected attendance Using the *Expected Value* knowledge point $$ \begin{aligned} E(X) &= (17000 \times 0.10) + (6000 \times 0.90) \ &= 1700 + 5400 \ &= 7100 \end{aligned} $$ It is expected that 7100 people will attend the concert. { "subject": "Mathematics", "question_type": "Fill-in-the-blank", "knowledge_point": [ "Mathematics", "Statistics", "Expected Value" ] }

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Explanation:

Calculate probability of no rain

Calculate expected attendance

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