The ages of the 32 recruits in police academy are normally distributed with a mean of 27 with a standard deviation of 2. what is the probability that a recruit is at least 31 years old?

Since it's a sample size, we use x, as the mean and s= standard deviation
            _
Given:  x =27, s = 2 and total sample = 32.
Probability that a recruit is at least 31 years old?

Let's calculate the Z score :
              _
         X - x              31 - 27
Z =  → Z =  → Z = 2 (now look up in the Z score table,
           s                      2

Area (Z=2) =0.9772 , but Z ≥ 2  (at least) , then :
Area (Z≥2) = Area (Z≤ - 2)  = 0.0228

P(≥31)= 0.0228