When Mendel conducted his famous genetics experiments with plants, one sample of 1064 offspring consisted of 787 plants with long stems and 277 plants with short stems. Mendel theorized that 25% of the offspring plants would have short stems.

a. If Mendel’s theory is correct, find the mean and standard deviation for the numbers of plants with short stems in such groups of 1064 offspring plants.

b. Are the actual results unusual? What do the actual results suggest about Mendel’s theory?