P (Z<1.56)= 0.94
Explanation:
Step 1: Sketch the curve.
The probability that X<74 is equal to the blue area under the curve.
Step 2:
Since μ=60 and σ=9 we have:
P ( X<74 )=P ( X−μ<74−60 )=P (X−μ/σ<74−60/9)
Since x−μ/σ=Z and 74−60/9=1.56 we have:
P (X<74)=P (Z<1.56)
Step 3: Using the standard normal table to conclude that:
P (Z<1.56)=0.9406 , rounding off to 2 decimals we get P (Z<1.56)= 0.94
