Probability that a randomly selected adult has an IQ less than 137 is 0.9452
Step-by-step explanation:
Step 1:
Sketch the curve.
The probability that X<137 is equal to the blue area under the curve.
Step 2:
Since μ=105 and σ=20 we have:
P ( X<137 )=P ( X−μ<137−105 )= P(X−μ/ σ< 137−105/20 )
Since x−μ/σ=Z and 137−105/20=1.6 we have:
P (X<137)=P (Z<1.6)
Step 3:
Use the standard normal table to conclude that:
P (Z<1.6)=0.9452
∴ probability that a randomly selected adult has an IQ less than 137 is 0.9452.
