Here is some code that will allow you to check your answers. For example if \(\bar{X} \sim \mathcal{N}(5,2)\) and you want to know what the \(Pr(\bar{X} < 3)\) is, you can use the following code. Meaning just change the mean and sd to fit the problem you are #working on.

pnorm(2, mean = 5, sd = 2)
## [1] 0.0668072

8.1

15

  1. Type answer here. Normal
  2. Type answer here. .0668
  3. Type answer here. .0179

  4. Type answer here. .7969 17

  5. Type answer here. The population must be normally distributed, mean of x should equal 64 and the standard deviation of x should = 17/(square root 12) or 4.907
  6. Type answer here. 0.7486

  7. Type answer here. 0.4052 19

  8. Type answer here. 0.3520
  9. Type answer here. Normal, mean of x =266, and the standard deviation of x = 16/square root of 20 which equals 3.578
  10. Type answer here. 0.0465
  11. Type answer here. 0.0040
  12. Type answer here. This sample came from a population whose mean gestation period was less than 266 days

  13. Type answer here. 0.9844 21

  14. Type answer here. 0.3085
  15. Type answer here. 0.0418
  16. Type answer here. 0.0071
  17. Type answer here. Increasing the sample size decreases the probability that x bar is greater than 95
  18. Type answer here. A mean reading rate is not unusual because the probability that x bar is greater than or equal to 92.8 is 10 %, which is not entirely significant

  19. Type answer here. 93.7 words 23

  20. Type answer here. 0.5675
  21. Type answer here. 0.7291
  22. Type answer here. 0.8051
  23. Type answer here. 0.8531

  24. Type answer here.

The chance of earning a positive rate of return increases as the investment time horizon increases ###Similarily you can use the above code to determine the \(Pr(\hat{P} < \hat{p})\)

8.2

11

  1. Type answer here. Sampling distribution is normal
  2. Type answer here. 0.1922

  3. Type answer here. 0.0047 12

  4. Type answer here. Normal
  5. Type answer here. .8264

  6. Type answer here. .5 13

  7. Type answer here. Distribution is normal
  8. Type answer here. 0.0040

  9. Type answer here. 0.0233 14

  10. Type answer here. Normal
  11. Type answer here. .9898

  12. Type answer here. .9394 15

  13. Type answer here. Two outcomes: order a meal in a foreign language, or without a foreign language–this is qualitative
  14. Type answer here. The individuals in the survey and their ability to order in a foreign language make this valid
  15. Type answer here. Distribution is normal
  16. Type answer here. 0.1977

  17. Type answer here. 0.0239 16

  18. Type answer here.

  19. Type answer here.

  20. Type answer here.

  21. Type answer here.

  22. Type answer here.

17

  1. Type answer here. Normal
  2. Type answer here. 0.3228
  3. Type answer here. 0.3198
  4. Type answer here. 0.0838