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. x bar is approximately normal with the sample mean 80 and the sample distribution 2.

  2. 0.0668

  3. 0.0179

  4. 0.7969

17

  1. The population must be normally distributed. If the population is normally distrubuted, the sampling distribution of x bar is also normally distributed with the sample mean 64 and the sample distribution approximately 4.907.

  2. 0.7486

  3. 0.4052

19

  1. 0.3520

  2. The sampling distribution of x bar is normal with the sample mean 266 and the sample distribution approximately 3.578.

  3. 0.0465

  4. 0.0040

  5. This would be abnormal meaning that the sample probably came from a population whose mean gestation period was less than 266 days.

  6. 0.9844

21

  1. 0.3085

  2. 0.0418

  3. 0.0071

  4. This would decrease P because the sample distribution decreases as n increases.

  5. This mean reading speed is not unusual because P is 0.1056. This means the new reading program is not much more efective than the old one.

  6. 93.7 words per minute.

23

  1. 0.5675

  2. 0.7291

  3. 0.8051

  4. 0.8531

  5. The likelihood 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. The sampling distribution of p hat is approximately normal with the sample mean 0.8 and the sample standard deviation approximately 0.046.

  2. 0.1922

  3. 0.0047

12

  1. The sampling distribution of p hat is approximately normal with the sample mean 0.65 and the sample standard deviation approximately 0.0337.

  2. 0.1867

  3. 0.0375

13

  1. The sampling distribution of p hat is approximately normal with the sample mean 0.35 and the sample standard deviation approximately 0.015.

  2. 0.0040

  3. 0.0047

14

  1. The sampling distribution of p hat is approximately normal with the sample mean 0.42 and the sample standard deviation approximately 0.0129.

  2. 0.0099

  3. 0.0606

15

  1. Qualitative with 2 possible outcomes which are order a meal in a foreign language and not to.

  2. The variability comes from the individuals in the survey and whether or not they can order a meal in a foreign language.

  3. The sampling distribution of p hat is approximately normal with the sample mean 0.47 and the sample standard deviation approximately 0.035.

  4. 0.1977

  5. 0.0239

16

  1. Qualitative with 2 possible answers of yes or no.

  2. The variability comes from whether or not the individuals are satisfied with their life.

  3. The sample distribution is approximately normal with the sample mean 0.82 and the sample standard deviation 0.0038.

  4. 0.2177

  5. Yes becausethe proportion would be 0.0344.

17

  1. The sampling distribution is approximately normal with the sample mean 0.39 and the sample standard deviation approximately 0.022.

  2. 0.3228

  3. 0.3198

  4. 0.0838