The amount of growth in a 15day period for a population of s

The amount of growth, in a 15-day period, for a population of sunflower plants was found to follow a normal distibution with mean 3.18cm and standard deviation of 0.53cm. In what range do the middle 90% of all growth values lie?

Solution

Note that              
      
Lower Bound = X - z(alpha/2) * s           
Upper Bound = X + z(alpha/2) * s       
              
where              
alpha/2 = (1 - confidence level)/2 =    0.05          
X = sample mean =    3.18          
z(alpha/2) = critical z for the confidence interval =    1.644853627          
s = sample standard deviation =    0.53          

              
Thus,              

Lower bound =    2.308227578          
Upper bound =    4.051772422          
              
Thus, the confidence interval is              
              
(   2.308227578   ,   4.051772422   ) [ANSWER]