In Europe, 53% of the flowers of the Rewardless Orchid, Dactylorhiza sambucina, are yellow, whereas the remaining flowers are purple. For this problem, only use the normal approximation where it is appropriate. Use the binomial distribution where the normal approximation is inappropriate. Required:
a. If we took a random sample of a single individual from this population, what is the probability that it would be purple?
b. If we took a random sample of five individuals, what is the probability that at least three are yellow?
c. If we took many samples of n=5 individuals, what is the expected standard deviation of the sampling distribution for the proportion of yellow flowers?
d. If we took a random sample of 263 individuals, what is the probability that no more than 150 are yellow?