After years of collecting sports cards, our friend Nick decides to open a shop. He sells packs of cards but he focuses on selling rare cards. Suppose that the distribution of the values of all rare cards is Normal with mean $61.00 and standard deviation $12.35. Because Nick has bought cards from all over the US, his personal collection can be considered random. A sample of 40 of his cards is chose. let x represent the average value of the sampled cards.
A) Give the mean and standard deviation of the sampling of distribution of x.
B) Do we need to be concerned about being able to invoke the Central Limit Theorem in this problem? Why or why not?
C) What is the probability that the average value of Nick's sample will be more than $70?
D) If Nick randomly chooses a SINGLE card, what is the probability that its value will be between $50 and $60?