Final answer:
The question pertains to statistics and the normal distribution of bread lengths in Subway's bread making process. It suggests confirming whether the lengths are normally distributed by checking if they fit the empirical rule. Hypothesis testing uses population parameters and sample statistics to calculate p-values and make inferences about the population.
Step-by-step explanation:
The question pertains to the field of statistics, a branch of mathematics dealing with data collection, analysis, interpretation, and presentation. The specific focus here is on the concept of the normal distribution, which is used to model various real-world phenomena, including process measurements like the lengths of bread in a Subway. The original question seems incomplete, but based on provided information, it seems to inquire about the bread lengths being normally distributed with a given mean and standard deviation.
Applying the concepts mentioned, in a normal distribution, approximately 68% of values lie within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations. This is known as the empirical rule. When examining the bread making process at Subway, one might check whether the bread lengths indeed follow this pattern to confirm if the process yields normally distributed lengths.
Moreover, in hypothesis testing scenarios like the examples provided, the population mean, sample mean, and sample standard deviation are used to calculate the probability (p-value) of observing the sample data, given that the null hypothesis is true. If this probability is very low (typically less than 5%), the null hypothesis can be rejected, suggesting the alternative hypothesis is likely true.