Probability that a person has an IQ of at least 130

Question

If IQ scores are normally distributed with a mean of 100 and a standard deviation of 20, then what is the probability that a person has an IQ score of at least 130? 

Answer 1

Calculate the z score if the IQ: z = (x-μ)/σ = (130-100)/20 = 1.5

 

Using the z-score table gives P(IQ < 130) = P(z < 1.5) = 0.9332

 

Therefore P(IQ ≥ 130) = 1 - 0.9332 = 0.0668