Question

for an outdoor concert by the city orchestra, concert organizers estimate that 19,000 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 30% chance of rain determine the expected number of people who will attend this concert. it is expected that people will attend the concert.

Explanation:

Step1: Calculate the probability of no - rain

The probability of rain is \(P(\text{rain}) = 0.3\). So the probability of no - rain is \(P(\text{no rain})=1 - 0.3=0.7\)

Step2: Use the formula for expected value

The formula for expected value \(E(X)=\sum_{i}x_{i}P(x_{i})\). Here, \(x_1 = 19000\) (number of people when no - rain) with \(P(x_1)=0.7\) and \(x_2 = 4000\) (number of people when rain) with \(P(x_2)=0.3\)

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Answer:

\(14500\)