1.) Miranda, a quality assurance inspector at a frozen treat factory, checks for product quality using a random sample of 11 frozen treats from a batch of 41, with 22 grape popsicles and 19 cherry popsicles. Letpbe the proportion of grape popsicles in the sample.

Part A:Is the 10% condition met in this case? Justify your answer.

Part B:Is the Normal condition met in this case? Justify your answer.

2.)Given a population mean of 27.1 with a standard deviation of 8.4 and a sample size of 10, answer these questions:

Part A:What is the standard deviation of the sampling distribution of x? Show your work.

Part B:What does the sample size need to be if you want the standard deviation of the sampling distribution of x to be 2.8? Show your work.