Assume that blood pressure readings are normally distributed

Assume that blood pressure readings are normally distributed with a mean of 115 and a standard deviation of 8. If 100 people are randomly selected, find the probability that their mean blood pressure will be less than 117.

Solution

We first get the z score for the critical value. As z = (x - u) sqrt(n) / s, then as          
          
x = critical value =    117      
u = mean =    115      
n = sample size =    100      
s = standard deviation =    8      
          
Thus,          
          
z = (x - u) * sqrt(n) / s =    2.5      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   2.5   ) =    0.993790335 [ANSWER]