Answer:
Step-by-step explanation:
1. Use a calculator with distribution functions here. We're interested in finding the area under the standard normal curve to the right of 590, given that the mean is 510 and the standard deviation is 80. Note that 590 = 510 + 80, meaning that 590 is 1 standard deviation above the mean.
According to the Empirical Rule, 68% of data under a standard normal curve lies within 1 standard deviation of the mean. The area from the extreme left of this curve to x = 510 is 0.500, and the additional area under the curve from 510 to 590 is 34% of the total area, or 0.340.
Thus, the desired area is 0.500 + 0.340 = 0.840. This represents the desired probability.
2. What percentile is a score of 750? Find the number of standard deviations to the left of 750:
750 - 510
z-score = ------------------- = 24/8 = 3.00
80
The desired percentile is the area to the left of z = 3.00. Using a calculator, we find this area to be 0.9987. That 750 score is in the 99+ percentile.
