use centarly limit theorum the lengths of pregency are norma

use centarly limit theorum the lengths of pregency are normally distributed with a mean of 264 days and a standard deviation of 15 days. if 36 women are randomly selected , find the probability that they have a mean pregrency between 264 days and 266 days

Solution

We first get the z score for the two values. As z = (x - u) sqrt(n) / s, then as          
x1 = lower bound =    264      
x2 = upper bound =    266      
u = mean =    264      
n = sample size =    36      
s = standard deviation =    15      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u) * sqrt(n) / s =    0      
z2 = upper z score = (x2 - u) * sqrt(n) / s =    0.8      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.5      
P(z < z2) =    0.788144601      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.288144601   [answer]