In Europe, 53% of flowers of the rewardless orchid, Dactylorhiza sambucina, are yellow, whereas the remaining flowers are purple (Gigord et al. 2001). For this problem, you may use the normal approximation only if it is appropriate to do so.

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^{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?