Final answer:
To find the probability that at least 8 out of 10 Americans say that they believe texting while driving should be outlawed, you can use the binomial distribution probability function. Calculate the probabilities for each possible number of successes (8, 9, 10) using the formula and sum them up to get the desired probability. Round the answer to four decimal places.
Step-by-step explanation:
To find the probability that at least 8 out of 10 Americans say that they believe texting while driving should be outlawed, we can use the binomial distribution probability function. The formula for the probability mass function (PMF) of the binomial distribution is:
P(X = k) = C(n, k) * p^k * (1 - p)^(n - k), where n is the number of trials, k is the number of successes, C(n, k) is the number of combinations, and p is the probability of success.
In this case, n = 10, k can be 8, 9, or 10 (since we want at least 8), and p is the probability that an American says texting while driving should be outlawed. Let's assume p = 0.5 for simplicity.
Using the formula, we can calculate the probabilities:
P(X = 8) = C(10, 8) * 0.5^8 * (1 - 0.5)^(10 - 8)
P(X = 9) = C(10, 9) * 0.5^9 * (1 - 0.5)^(10 - 9)
P(X = 10) = C(10, 10) * 0.5^10 * (1 - 0.5)^(10 - 10)
Finally, we sum up these probabilities to get the probability that at least 8 out of 10 Americans say that they believe texting while driving should be outlawed:
P(X ≥ 8) = P(X = 8) + P(X = 9) + P(X = 10)
Calculating these probabilities using the provided formula and rounding the answer to four decimal places, we can find the desired probability.