# Math Statistics

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3. Suppose 20% of all heart transplant patients do not survive the operation.
a. Think about taking repeated random samples of 371 patients from this population.
Describe how the sample proportion who die would vary from sample to sample. (Hint: Be sure to refer to the shape, center, and spread of its sampling distribution.) Also include a well-labeled sketch to represent this distribution.
b. Suppose you take a random sample of 371 heart transplant patients. Determine the probability that the sample proportion who die would be .213 or higher.

4. Suppose I tell you that I flipped a coin multiple times and got 75% heads. Would you be reasonably convinced that this was not a fair coin (where “fair” means that the coin has a 50/50 chance of landing heads or tails)? If so, explain why. If not, describe what additional information you would ask for and explain why that information is necessary.

5. The distribution of house prices is skewed to the right because most houses cost a modest amount but a few cost a very large amount. If you take a random sample of 1000 houses, can you reasonably expect the distribution of the house prices to be approximately normal? Explain your answer.

6. Suppose you flip a fair coin until it lands heads up for the first time. It can be shown (do not try to calculate this) that the expected value of the number of flips required is 2. Explain (with a sentence or two) what this expected value means in this context.