Let X be the amount won or lost in betting 5 on red in roule

Let X be the amount won or lost in betting $5 on red in roulette. Then

Solution

Consider:

Thus,  
  
E(x) = Expected value = mean =    -0.263157895

Var(x) = E(x^2) - E(x)^2 =    24.93074792

s(x) = sqrt [Var(x)] =    4.99306999

Now, this question is like asking the probability of a mean loss of -50/100 = -0.50.

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    -0.5      
u = mean =    -0.263157895      
n = sample size =    100      
s = standard deviation =    4.99306999      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -0.474341648      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -0.474341648   ) =    0.682371852 [ANSWER]