What is the expected value of X. After finishing the competition in 34th place y

Question

What is the expected value of X.

After finishing the competition in 34th place you have a little extra spending money to have fun with in Vegas. Deciding to take a break from the gambling you are looking into booking a helicopter tour of the Grand Canyon. As part of a promotional deal the tour company is offering you a spin at the coupon wheel. One spin costs $8 and will be good for a tour discount based on where the wheel stops. The table below shows the probability distribution of the discounts.

Explanation / Answer

A)

Consider the table:      
      
x   P(x)   x P(x)
0   0.1   0
4   0.25   1
8   0.5   4
16   0.1   1.6
32   0.05   1.6
      
      
Totals       8.2
       =E(x)
      
Thus,      
      
E(x) =    8.2   [ANSWER]

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B)

As the expected discount is greater than the spin price, then it is profitable. YES, YOU SHOULD PURCHASE A SPIN.

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