Final answer:
The question deals with statistical concepts such as probabilities of events, hypothesis testing at a significance level, and the calculation of confidence intervals and sample sizes in a business context. These statistical tools help businesses make informed decisions based on data analysis.
Step-by-step explanation:
The question falls under the realm of probability and statistics, particularly focusing on the concepts of random sampling, confidence intervals, and hypothesis testing. The subject matter relates to the mathematical understanding and application of probabilities and statistical analysis in business contexts, such as call volumes and customer satisfaction metrics in small companies. Understanding the probability that employees make more than 20 long-distance calls during peak time requires a distribution model and relevant statistics. Hypothesis testing at a 5 percent significance level involves evaluating evidence against a null hypothesis to make decisions regarding claims about waiting times. Confidence intervals and sample sizes are statements about the precision of sample estimates and their closeness to the population parameter, which scales with the desired level of confidence and the variability of the data.
When calculating the required number of customers to survey to achieve certain confidence and precision, the sample size calculation would change based on the level of confidence and the allowable margin of error. A requirement of higher confidence level or a smaller margin of error generally leads to a larger sample size requirement. Similarly, when predicting the mean excess time used, understanding the 95th percentile gives us information about the distribution of the sample mean excess time used.