Question

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?

Answer 1

a. The probability of taking out a purple flower is 0.47.

b. The probability that out of a sample of 5 flowers at least 3 flowers are yellow 0.56.

c. The standard deviation of the distribution for proportion of yellow flowers is 0.22.

d. The probability that out of the 263 samples, at most 150 of them are yellow is 0.90.

Explanation: