Question

In a recent year, the Better Business Bureau settled 75% of complaints they received. You have been hired by the Bureau to investigate complaints this year involving computer stores. You plan to select a random sample of complaints to estimate the proportion of complaints the Bureau is able to settle. Suppose your sample size is 237. What is the probability that the sample proportion will be at most 3 percent more than the population proportion? 4 decimal places

Answer 1

To calculate the probability that the sample proportion is within 3% more than the population proportion, use the normal approximation to the binomial distribution with the given sample size and known population proportion, then find the associated z-score and use the standard normal distribution.

Step-by-step explanation:

The question deals with finding the probability that the sample proportion will be at most 3 percent more than the population proportion, given that the sample size is 237. To address this, one would typically use the normal approximation to the binomial distribution because the sample size is large.

Since the population proportion that the Better Business Bureau settled is 75%, any sample proportion up to 78% (which is 3% more) would be considered. The formula to find the z-score for the sample proportion p' is given by:

Z = (p' - p)/√(pq/n)

Where p is the population proportion, q is 1-p, and n is the sample size. Once we have the z-score, we use the standard normal distribution to find the probability associated with that z-score. Calculating the exact probability without the values of the sample proportion or standard deviation is not possible. However, the process has been clearly outlined for you to apply the relevant statistics.