Beet farmers claim that 76% of vegetarians like beets, while only 41% of carnivores like beets. Suppose a random samples of 21 vegetarians and 31 carnivores are asked if they like beets. Let p hat Subscript Upper V and P hat Subscript c be the sample proportions of vegetarians and carnivores, respectively, who like beets. Which of the following is the correct shape and justification of the sampling distribution of p hat Subscript Upper V Baseline minus p hat Subscript c ?

A, bimodal because one population proportion is centered at 0.76, while the other is centered at 0.41
B. approximately Normal because the expected numbers of successes and failures for each sample are all at least 10
C. not approximately Normal because the expected numbers of successes and failures for each sample are all at least 10
D. not approximately Normal because the expected numbers of successes and failures for the vegetarian group are not both at least 10