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. 14/7 = 2

  2. 0.0668

  3. 0.0179

  4. 0.7969

17

  1. 4.907

  2. 0.7493

  3. 0.403

19

  1. 80

  2. 0.0668

  3. 0.0179

  4. 0.7969

  5. that the mean is within the standard deviation

  6. 42 21

  7. Type answer here.

  8. Type answer here.

  9. Type answer here.

  10. Type answer here.

  11. Type answer here.

  12. Type answer here.

23

  1. .309

  2. 2.89

  3. 2.04

(d)when the sample size increases the probablitiy of the event decreases because sigma decreases as n increases?

  1. that thethere is a 5% chance thatt the mean will exceed 93.7 wpm

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

8.2

11

  1. mean sampling disribution is 0.8. sD of sampling distsribution is 0.8x0.2/75

  2. 0.1922

  3. 0.0047

12

  1. the mean of the Sampling distribution is 0.65 the SD of the sampling distribution is 0.0337

  2. 0.1867

  3. 0.0375

13

  1. mean of sampling proportion =.35 SD of sampling proportion = 0.35x0.65/1000

  2. 0.0040

  3. 0.0233

14

  1. mean of sampling proportion =.042 SD of sampling proportion = 0.42x0.58/1460

  2. 0.0102

  3. 0.0606

15

  1. the mean of the sampling distribution = 0.47 the standard deviation =0.03529

  2. 0.1977

  3. yes the americans who can order a meal is greater than 0.5 20/100 americans can so 80 would be unusual

  4. Type answer here.

  5. Type answer here.

16

  1. the distribution is normal with mean =0.82 standard deviation = 0.0384

  2. 0.781

  3. the probablitiy of americans who are satisfied is less than 75 are 0.0342 this shows about 3 out of 100 beleive that life is going well.

  4. Type answer here.

  5. Type answer here.

17

  1. A random sample of size 500 americans is less than 5% of the population. the SD = 0.0218

  2. -0.459

  3. 0.459

  4. the probability 500 adults to result in 210 adults agreeing marraige is obsolete is 0.0837 this means about 8 out of 100 random samples of adult americans to result in 21/ 0 americans who believe marriage is obsolete