Tickets to minor league baseball games cost on average 702 I

Tickets to minor league baseball games cost on average $7.02. Including food, drinks, parking, and other expenses, the average cost for a family of four to attend the game is $57.70. Assume the distribution of cost has a normal distribution with standard deviation $5.57. The approximate proportion (using the standard normal table) of people that will pay between $60 and $70 is:

Solution

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    60      
x2 = upper bound =    70      
u = mean =    57.7      
          
s = standard deviation =    5.57      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    0.412926391      
z2 = upper z score = (x2 - u) / s =    2.208258528      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.660169728      
P(z < z2) =    0.986386872      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.326217144   [ANSWER]