Final answer:
To find the probability that exactly three families say that their children have an influence on their vacation plans, we will use the binomial probability formula. The probability of one family saying that their children have an influence on their vacation plans is 57%. Using the binomial probability formula, the probability that exactly three families say that their children have an influence on their vacation plans is approximately 0.2136, or 21.36%.
Step-by-step explanation:
To find the probability that exactly three families say that their children have an influence on their vacation plans, we will use the binomial probability formula. First, we need to calculate the probability of one family saying that their children have an influence on their vacation plans, which is 57%. Then, we can use the formula to calculate the probability of getting exactly three families out of eight. The formula is:
P(X=k) = C(n, k) * p^k * (1-p)^(n-k)
Where:
- P(X=k) is the probability of getting k successes
- n is the number of trials (in this case, the number of families)
- k is the number of successes (in this case, 3)
- p is the probability of success (in this case, 0.57)
Using the formula, we can calculate:
P(X=3) = C(8, 3) * 0.57^3 * (1-0.57)^(8-3)
P(X=3) = 56 * 0.57^3 * (1-0.57)^5
P(X=3) ≈ 0.2136
Therefore, the probability that exactly three families say that their children have an influence on their vacation plans is approximately 0.2136, or 21.36%.