Key to Practice Midterm 2

Problem 1
A.  False, arcsinx is not defined for |x| < 1.
B.  False, cosh2x - sinh2x = 1

Problem 2

Problem 3

Problem 4
A.  -1/2 sqrt[16 - x4] + C
B.  1/9 arcsin[(3x3)/5] + C
C.  arctanh(ex) + C

Problem 5
By the inverse formula, and the appropriate triangle.

Problem 6
400,000,000 mile-pounds

 Review for Midterm II

  1. Explain how to find P(a < x < b) when given the graph of the a probability distribution function.

  2. Name three attributes of the normal distribution.

  3. What does the Central Limit Theorem say about the distribution of the sample means?  When does the Central Limit Theorem apply?

  4. What does the Central Limit Theorem say about the distribution of the sample proportion? When does the Central Limit Theorem apply?

  5. Why would one want to use a confidence interval?

  6. How does one come up with a confidence interval for the population mean?

  7. How does one come up with a confidence interval for the population proportion?

  8. When must one use a t statistic instead of a z statistic?  When can neither be used?

  9. What are the different types of Hypothesis tests and why are they used?