1. Why is the probability that a continuous random variable is equal to a single number zero? (i.e. Why is P(X=a)=0 for any number a) [1 sentence]
2. In what ways can a quick drawing of the normal curve (not a detailed empirical rule drawing but a simple one like that shown in the instructor's video) be used to estimate or verify your answer to a problem like practice exercises 2-4? [2 sentences]
3. The empirical rule says that 95% of the population is within 2 standard deviations of the mean, but when I find the z-scores that mark off the middle 95% of the standard normal distribution I calculate -1.96 and 1.96. Is this a contradiction? Why or why not? In other words why are the normal distribution calculators not agreeing with the empirical rule? [2 sentences]
4. What does a z-score tell you about a number in a data set? [1 sentence]
5. What two quantities do we need to fully describe a normal distribution? [1 sentence]
6. How is probability determined from a continuous distribution? Why is this easy for the uniform distribution and not so easy for the normal distribution? [2 sentences]
7. What does the symmetric bell shape of the normal curve imply about the distribution of individuals in a normal population? [2 sentences]
8. How can the empirical rule be restated in terms of z-scores and percentiles? Restate it for four of the seven z-scores. Hint: Use the definitions of z-score and percentile and avoid use of the phrase "standard deviation" or the numbers 68, 95, and 99.7. [4 statements]