Data with 860 observations are drawn from a bellshaped distr

Data with 860 observations are drawn from a bell-shaped distribution with a mean of 76 and a standard deviation of 18. Approximately how many observations are more than 112? (Round your answer to the nearest whole number.)

Solution

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    112      
u = mean =    76      
          
s = standard deviation =    18      
          
Thus,          
          
z = (x - u) / s =    2      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   2   ) =    0.022750132

Hence, around 0.022750132*860 = 19.56511352 or around 20 [ANSWER, 20]