Final answer:
To calculate the probability that more than 447 homes out of a survey of 1000 are served by the satellite company, one should use the normal approximation to the binomial distribution, calculate the mean and standard deviation, find the z-score for 447, and reference a standard normal distribution table to obtain the probability.
Step-by-step explanation:
The question is about calculating the probability that more than 447 out of 1000 homes in a survey are served by the satellite company, given that the satellite company serves 43% of homes in the area. To find this probability, one would typically use the normal approximation to the binomial distribution because the sample size is large. We need to calculate the mean (μ = np) and standard deviation (σ = √np(1-p)) of the distribution, where n is the sample size and p is the probability of a home being served by the satellite company. For n = 1000 and p = 0.43, we'll have μ = 430 and σ ≈ 15.77.
Next, we calculate the z-score for 447, which is (447 - μ) / σ. Once we have the z-score, we can use a standard normal distribution table or calculator to find the probability that the z-score is above this calculated value. This will give us the probability that more than 447 homes are served by the satellite company.
Without the actual calculations being performed here, to answer the student's question, they would need to use the steps outlined above to find the specific probability value.