a normal distribution has a mean of u 70 with o12 if one sco

a normal distribution has a mean of u= 70 with o=12. if one score is randomly selected from this distribution, what is the probability that the sore will be less than x= 76?

Solution

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    76      
u = mean =    70      
          
s = standard deviation =    12      
          
Thus,          
          
z = (x - u) / s =    0.5      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   0.5   ) =    0.691462461 [ANSWER]