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. Central Limit Thereom says the distribution is approximately normal.

  2. .0668

  3. .0179

  4. .7969

17

  1. Populatiion must be normally distriubuted. If this is the case the sampling distribution of the mean the sd is exactly normal. The mean and sd of the sampling distribution are ux=u=64 and ox = 4.907.

  2. .7486

  3. .4052

19

  1. .3520

  2. 3.578

  3. .0465

  4. .0040

  5. Answers will vary, but due to the fact that d indicates it was unusual we would conclude it likely came from a sub 266 day gestation period.

  6. .9844

21

  1. .3085

  2. .0418

  3. .0071

  4. It descreased the probability that mean >95 because n increases as ox decreases.

  5. No, would not be unusual because the proability the mean is greater than 92.8 is .1056.

  6. c = 93.7 words per minute

23

  1. .5675

  2. .7291

  3. .8051

  4. .8531

  5. 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. n = 75, np(1-p) = 12 >10, distribution is approximately normal, mean is .08, and SD = .046

  2. .1932

  3. .0047

12

  1. Type answer here.

  2. Type answer here.

  3. Type answer here.

13

  1. Distribution approximately normal, mean = .35, and SD = .015.

  2. .0040

  3. .0233

14

  1. Type answer here.

  2. Type answer here.

  3. Type answer here.

15

  1. Response is qualitative with teo possible outcomes, can order a meal in a foreign language or not.

  2. Sample proportion is a random variable because it varies from sample to sample. Source of the variability is the individuals in the sample and their ability to order a meal in a foreign language.

  3. SD = .035

  4. .1977

  5. .0239

16

  1. Type answer here.

  2. Type answer here.

  3. Type answer here.

  4. Type answer here.

  5. Type answer here.

17

  1. SD = .022

  2. .3228

  3. .3198

  4. .0838