Within a population, IQ score has a normal distribution with a mean of μ=100 and a standard deviation of σ=15 . Apply the Empirical Rule to find the probability that an individual has an IQ score above 130.(1 point)
Using the Empirical Rule, we know that approximately 68% of the population lies within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
Since we are looking for the probability of an individual having an IQ score above 130, we want to find the probability of being above 130 which is beyond 2 standard deviations from the mean.
So, first calculate the z-score for an IQ score of 130:
z = (130 - 100) / 15 = 2
Since a z-score of 2 falls within the range of 2 standard deviations from the mean, we know that the probability of having an IQ score above 130 is approximately 2.5% based on the Empirical Rule.
Therefore, the probability that an individual has an IQ score above 130 is 2.5%.