Question

A rock concert producer has scheduled an outdoor concert. The producer estimates the attendance will depend on the weather according to the following table.

Answer 1

Answer:

$\begin{gathered} a)\text{ 36,100} \\ b)\text{ \ 186,500} \end{gathered}$

Explanation:

a) Here, we want to get the expected attendance

We have to multiply the probability of each attendance by the number of attendees, then sum

We have that as:

$\begin{gathered} 0.1(6000)\text{ + 0.2\lparen25000\rparen + 0.2\lparen15000\rparen + 0.5\lparen55000\rparen} \\ =\text{ 36,100} \end{gathered}$

b) To get the expected profit, we multiply the cost of each ticket by the number of attendees, then subtract the cost of setting up the concert

We have that as:

$\begin{gathered} 36100(15)-(55000\text{ + 300000\rparen} \\ =\text{ \ 186,500} \end{gathered}$