Final answer:
The probability of getting no more than one bad grapefruit in a sack can be calculated by considering the probability of no bad grapefruits and exactly one bad grapefruit. The probability of getting at least one good grapefruit can be found by taking the complement of getting no good grapefruits. The expected number of good grapefruits in a sack can be calculated by multiplying the probability of getting a good grapefruit by the number of grapefruits in a sack.
Step-by-step explanation:
A) To find the probability of getting no more than one bad grapefruit in a sack, we need to consider two situations: either there are no bad grapefruits or there is exactly one bad grapefruit in the sack. The probability of no bad grapefruits is 85% (good grapefruit) raised to the power of 7 (number of grapefruits in a sack). The probability of exactly one bad grapefruit is (85% raised to the power of 6) multiplied by 15% (bad grapefruit). Therefore, the probability of getting no more than one bad grapefruit is the sum of these two probabilities.
B) To find the probability of getting at least one good grapefruit, we need to find the complement of getting no good grapefruits, which is 1 minus the probability of getting no good grapefruits.
C) The expected number of good grapefruits in a sack can be calculated by multiplying the probability of getting a good grapefruit (85%) by the number of grapefruits in a sack (7).
D) The standard deviation of the r probability distribution can be calculated using the formula sqrt(npq), where n is the number of trials (7), p is the probability of success (85%), and q is the probability of failure (15%).