Last Updated on May 5, 2023
GMAT OFFICIAL GUIDE PS
Solution:
This problem is testing us on symmetric distributions.
In any symmetric distribution with mean m and standard deviation d, 50% of the data values lie below the mean, and the other 50% lie above the mean. Furthermore, if p percent of the data values lie within k standard deviations of the mean, then p/2 percent of the data values lie between m and m – kd, and the other p/2 percent lie between m and m + kd. For example, if 20% of the data values lie within 1 standard deviation of the mean, then 10% of the data values lie between m and m – d and the other 10% lie between m and m + d.
So here, we want to find the percent of the distribution that is less than m + d. We know that 50% of the data values lie below m. We also know that since 68% of the data values lie within 1 standard deviation of the mean, 68%/2 = 34% of the data values lie between m and
m + d. Therefore, there is a total of 50% + 34% = 84% of the distribution that is less than m + d. See the diagram below.
Answer: D
