Problem 4 The average height of students has a normal distri

(Problem 4) The average height of students has a normal distribution with a standard deviation of 2.5 inches. You want to estimate the mean height of students at your college to within 1-inch with 95% confidence. How many students should you measure? HINT: Be sure to consider the two-tail probability when evaluating the z-score for the confidence level. (10 points)

Solution

Note that      
      
n = z(alpha/2)^2 s^2 / E^2      
      
where      
      
alpha/2 = (1 - confidence level)/2 =    0.025  
      
Using a table/technology,      
      
z(alpha/2) =    1.959963985  
      
Also,      
      
s = sample standard deviation =    2.5  
E = margin of error =    1  
      
Thus,      
      
n =    24.00911763  
      
Rounding up,      
      
n =    25   [ANSWER]