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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?

User Cryptjar
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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 :
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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
User Malvadao
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