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
