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. The sample distribution is normal, with a mean of 80 and a standard deviation of 2.

  2. 6.68% (0.0668)

  3. 1.79% (0.0179)

  4. 79.75% (0.7976)

17

  1. The population must be normally distributed. The sampling distribution is approximately 4.9075.

  2. 74.86% (0.7486)

  3. 40.52% (0.4052).

19

  1. 35.2% (0.5320)

  2. The sampling distribution would be approximately 3.578

  3. 4.65% (0.0465)

  4. .4% (0.0040)

  5. There’s a very low probability of this (.4%); for it to happen, the population sampled would have to have a mean gestation less than 266.

  6. 98.44% (0.9844)

21

  1. 30.85% (0.3085)

  2. 4.18% (0.0418)

  3. 99.27% (0.9927)

  4. .71% (0.0071)

  5. Since a random sample of 20 has a 10.56% probability of having a sample mean of 92.8wpm or higher, it is does not clearly indicate that the new program is improving students’ wpm.

  6. 93.69 wpm

23

  1. 56.75% (0.5675)

  2. 72.91% (0.7291)

  3. 80.51% (0.8051)

  4. 85.31% (0.8531)

  5. The likelihood of a positive rate of return increases over time.

Similarily you can use the above code to determine the \(Pr(\hat{P} < \hat{p})\)

8.2

11

  1. ~ normal, standard dev = 0.046, mean = 0.8

  2. 19.22% (.1922)

  3. 0.47% (0.0047)

12

  1. ~ normal, standard dev = 0.3373, mean = 0.65

  2. 18.67% (.1867)

  3. 3.75% (.0375)

13

  1. ~ normal, standard deviation = 0.015, mean = 0.35

  2. .4% (0.004)

  3. 2.33% (0.0233)

14

  1. ~ normal, standard dev = 0.0129, mean = .42

  2. 1.02% (0.0102)

  3. 6.06% (0.0606)

15

  1. Qualitative, because the data points that can be collected are “yes” and “no.”

  2. It’s a random variable because whether the people in the sample can order in another language is a source of variability.

  3. ~ normal, standard deviation = .035291642, mean = .47

  4. 19.77% (0.1977)

  5. Yes, because it has a probability of 2.39% (0.0239)

16

  1. Qualitative, because the data points that can be collected are either “yes” or “no.”

  2. It’s a random variable because whether the people in the sample are satisfied with the way things are going in their lives is a source of variability.

  3. ~ normal, standard deviation = 0.0384, mean = .82

  4. 21.77% (0.2177)

  5. Yes, because it has a probability of 3.44% (0.0344)

17

  1. ~ normal, standard deviation = 0.02181284, mean = .47

  2. 32.28% (0.3228)

  3. 31.98% (0.3198)

  4. 8.38% (0.0838)