Students scores on the STAAR test for math are believed to b

Students scores on the STAAR test for math are believed to be normally distributed with a mean of 73 and standard deviation of 9

Suppose that 30 students are randomly selected and all take the STAAR test. Compute the probability that the mean score for this group is greater than 80.

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    80      
u = mean =    73      
n = sample size =    30      
s = standard deviation =    9      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    4.260064336      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   4.260064336   ) =    1.02184*10^-5 [ANSWER]