Final answer:
To solve this problem, we will use the binomial probability formula. For part (a), we calculate the probability of exactly six U.S. adults having very little confidence in newspapers. For part (b), we calculate the probability of at least four U.S. adults having very little confidence in newspapers. For part (c), we calculate the probability of less than five U.S. adults having very little confidence in newspapers.
Step-by-step explanation:
To solve this problem, we will use the binomial probability formula.
(a) To find the probability that exactly six U.S. adults have very little confidence in newspapers, we use the formula:
P(X=k) = C(n, k) * p^k * (1-p)^(n-k)
Here, n = 8 (the number of trials), k = 6 (the number of successful outcomes), and p = 0.34 (the probability of success).
Plugging in these values, we get:
P(X=6) = C(8, 6) * 0.34^6 * (1-0.34)^(8-6)
Calculating this expression gives us the probability that exactly six U.S. adults have very little confidence in newspapers.
(b) To find the probability that at least four U.S. adults have very little confidence in newspapers, we need to calculate the probabilities of having exactly four, five, six, seven, and eight U.S. adults with very little confidence in newspapers. We add up these probabilities to get the total probability of having at least four U.S. adults with very little confidence in newspapers.
(c) To find the probability that less than five U.S. adults have very little confidence in newspapers, we need to calculate the probabilities of having zero, one, two, three, and four U.S. adults with very little confidence in newspapers. We add up these probabilities to get the total probability of having less than five U.S. adults with very little confidence in newspapers.