First, recognize that the mean does not change. The data added is symmetrical around the original mean of 64 days. The 4 new eggs with a 64-day incubation period will not affect the average. There are 2 new eggs with a 61-day incubation period and 2 new eggs with a 67-day incubation period. Both 61 and 67 are the same distance from the mean (3 days) and the number added is the same at both data points (2 eggs), so they will not change the average either.
Another way to confirm this is to find the average of the new eggs:
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GRE average.jpg [ 24.8 KiB | Viewed 1271 times ]
Next, consider the original data set and how it changes with the addition of the 8 new eggs. If the standard deviation were to remain the same, the distribution of the new data added would have to mirror the normal distribution of the original data set. In other words, about 68% would be within 1 day, 95% within 2 days, and 99.7% within 3 days. The new data added, however, is more spread out. The new data set's standard deviation will be greater than the original data set's of 1 day; therefore, the correct answer is (B)