a sample n4 is selected from a population with mean of 70 an

a sample n=4 is selected from a population with mean of 70 and standard deviation of 10. the probability of obtaining a sample mean greater than 65 is p= 0.8413

true or false

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    65      
u = mean =    70      
n = sample size =    4      
s = standard deviation =    10      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    -1      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   -1   ) =    0.841344746 = 0.8413

Thus, it is TRUE. [ANSWER]