Within a population, score has a normal distribution with a mean of mu = 100 and a standard deviation of sigma = 15 Apply the Empirical Rule to find the probability that an individual has an score above 130.
According to the Empirical Rule, approximately 68% of the data falls within one standard deviation of the mean, approximately 95% falls within two standard deviations of the mean, and approximately 99.7% falls within three standard deviations of the mean in a normal distribution.
To find the probability that an individual has a score above 130, we first need to calculate how many standard deviations 130 is above the mean:
Z = (X - mu) / sigma
Z = (130 - 100) / 15
Z = 2
So, a score of 130 is 2 standard deviations above the mean.
Since 95% of the data falls within two standard deviations of the mean, we can say that the probability of having a score above 130 is approximately:
1 - 0.95 = 0.05
Therefore, there is approximately a 5% chance that an individual has a score above 130 in this population.