A final exam in Statistics has a mean of 73 with a standard

A final exam in Statistics has a mean of 73 with a standard deviation of 7.73. Assume that a random sample of 24 students is selected and the mean test score of the sample is computed. What percentage of sample means are less than 70?

Please show the work, i\'m confused. Thanks

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    70      
u = mean =    73      
n = sample size =    24      
s = standard deviation =    7.73      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -1.901285699      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -1.901285699   ) =    0.028632301 [ANSWER]