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 4000 people will attend. on the day of the concert, meteorologists predict a 40% chance of rain. determine the expected number of people who will attend this concert.

it is expected that people will attend the concert.

Explanation:

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<reasoning>

Define the variables and probabilities

\[

$$\begin{aligned} &P(\text{Rain}) = 0.40 \\ &P(\text{No Rain}) = 1 - 0.40 = 0.60 \\ &X(\text{Rain}) = 4000 \\ &X(\text{No Rain}) = 17000 \end{aligned}$$

\]

Calculate the expected value

\[

$$\begin{aligned} E(X) &= P(\text{Rain}) \cdot X(\text{Rain}) + P(\text{No Rain}) \cdot X(\text{No Rain}) \\ E(X) &= 0.40 \cdot 4000 + 0.60 \cdot 17000 \\ E(X) &= 1600 + 10200 \\ E(X) &= 11800 \end{aligned}$$

\]
</reasoning>

<answer>
It is expected that <blank>11800</blank> people will attend the concert.
</answer>

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Answer:

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<reasoning>

Define the variables and probabilities

\[

$$\begin{aligned} &P(\text{Rain}) = 0.40 \\ &P(\text{No Rain}) = 1 - 0.40 = 0.60 \\ &X(\text{Rain}) = 4000 \\ &X(\text{No Rain}) = 17000 \end{aligned}$$

\]

Calculate the expected value

\[

$$\begin{aligned} E(X) &= P(\text{Rain}) \cdot X(\text{Rain}) + P(\text{No Rain}) \cdot X(\text{No Rain}) \\ E(X) &= 0.40 \cdot 4000 + 0.60 \cdot 17000 \\ E(X) &= 1600 + 10200 \\ E(X) &= 11800 \end{aligned}$$

\]
</reasoning>

<answer>
It is expected that <blank>11800</blank> people will attend the concert.
</answer>

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