Answer:
The probability is 0.0014
Step-by-step explanation:
When we have two possible outcomes p, q and we repeat the experiment multiple times, we apply the Binomial distribution, in this distribution the probability of getting exactly k successes in n trials is given by
where p represents the probability of success. nCk refers to the combinations of k elements out of n elements.
In this case, p= .29 (the probability that the person says "yes" being confident that passenger trips to the moon will occur in their lifetime.
q = .71 (The probability that the person says "no")
We sample 200 americans, therefore, we have n = 200 and we need the probability that less than 40% of the people sampled answer "yes".
The 40% of 200 is 80. So, in other words, we need less than 80 people to answer yes to the question.
P(x<80) = P(x=0) + P(x=1) + P(x=2) + .... + P(x=79) = 0.00143466294 (we can use a Binomial Distribution calculator to compute this result)
Therefore, P(x < 80) = 0.0014
