Final answer:
The probabilities for different numbers of TV's in a household, which follows a binomial distribution with parameters n=8 and p=10%, can be calculated using the binomial probability formula and adding or subtracting to find cumulative probabilities as needed.
Step-by-step explanation:
The question involves finding probabilities for a binomial distribution with parameters n=8 and p=0.10. For any given number of TVs (k), the probability can be found using the binomial probability formula:
P(X=k) = C(n, k) * p^k * (1-p)^(n-k)
Where C(n, k) is the combination of n items taken k at a time.
- a) Probability of 2 or 6 TVs: We calculate for P(X=2) and P(X=6) separately and then add them together since these are two distinct outcomes.
- b) Probability of 4 or fewer TVs: We sum up P(X=k) for k=0 through k=4.
- c) Probability of 2 or more TVs: Here, we can find P(X < 2) and subtract it from 1 (the total probability) to get P(X ≥ 2).
- d) Probability of fewer than 6 TVs: This will be the cumulative probability of P(X=0) through P(X=5).
- e) Probability of more than 4 TVs: Similarly, we can find P(X ≤ 4) and subtract from 1 to get P(X > 4).
To calculate these probabilities, one can use a binomial probability table, a calculator with a binomial probability function, or manual calculations using the formula provided.