Final answer:
Beth can infer the population mean of sit-ups for tenth-grade girls using her sample of 20 students. She would likely use a confidence interval or hypothesis test, taking into account the normal distribution of the data and a potential margin of error.
Step-by-step explanation:
Yes, Beth can make an inference about the population mean for all tenth-grade girls based on the sample of 20 fellow intramural tennis players. Since the number of sit-ups is normally distributed, as long as her sample is random and the sample size is not too small, she can use statistical methods like constructing a confidence interval or performing a hypothesis test to estimate the population mean. However, it's important to understand that this inference comes with a margin of error and a level of confidence, as it is based on just a sample of the entire population.
To construct a confidence interval or perform a hypothesis test, Beth will need to know or assume the population standard deviation or use the sample standard deviation. If she uses the sample standard deviation, the confidence interval construction or hypothesis test would need to use the t-distribution instead of the normal distribution since she has a sample of fewer than 30, which is considered a small sample size for these purposes.