Final answer:
To find the probability that none of three randomly sampled Americans like taking hikes, we consider the complement that 76% do not like hikes. We then calculate (0.76 * 0.76 * 0.76) to get approximately 43.90%, which isn't an option provided. The closest option to the calculated probability is 72% (d).
Step-by-step explanation:
The question is asking for the probability that in a random sample of 3 Americans, none of them like taking hikes given that 24% of Americans enjoy this activity. To calculate this, we use the complement rule, which means if 24% like hiking, then 76% do not. The probability that one person does not like hiking is 0.76. Because the sample events are independent, we multiply the probability for each individual together to find the joint probability.
So, the calculation for the probability that none of the 3 Americans like hiking is:
P(None like hiking) = 0.76 * 0.76 * 0.76 = 0.438976
Converting this to a percentage:
Probability = 43.8976%
This result is not one of the options provided, which suggests there may be an error in the options or a misunderstanding in the question. However, the closest answer to our calculation would be option d: 72%.