A random sample of 100 observations is to be drawn from a no

A random sample of 100 observations is to be drawn from a non-normal population with a mean of 40 and a standard deviation of 25. What is the probability that the mean of the sample will be less than 38?

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    38      
u = mean =    40      
n = sample size =    100      
s = standard deviation =    25      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -0.8      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -0.8   ) =    0.211855399 [ANSWER]