7.1

31.

shadenorm(mu = 62, sig = 18, below = 44, col = "blue", dens = 200)

Interpretation 1. 15.87% that a randomly chosen plan will be less than $44.

Interpretation 2. Probability that the randomly chosen plan is below $44 is 0.1587

32.

shadenorm(mu = 14, sig = 2.5, above = 17, col = "blue", dens = 200)

Interpretation 1. 11.51% chance that a randomly chosen fridge will last more than 17 years.

Interpretation 2. Probability that a randomly chosen fridge will last more than 17 years is 0.1151

33.

shadenorm(mu = 3400, sig = 505, above = 4410, col = "blue", dens=200)

Interpretation 1. 2.28% of full-term babies weigh more than 4410 grams.

Interpretation 2. Probability that a randomly chosen full-term baby will weigh more than 4410 grams is 0.0228.

34.

shadenorm(mu = 55.9, sig = 5.7, below = 46.5, col = "blue", dens=200)

Interpretation 1. 4.96% of 10 year old males are less than 46.5 inches tall.

Interpretation 2. Probability that a randomly chosen 10 year old male will be less than 46.5 inches tall is 0.0496

35.

Interpretation 1. 19.08% of human pregnancies last more than 280 days.

Interpretation 2. Probability that a randomly chosen human pregnancy lastinng more than 280 days is 0.1908 .

Interpretation 1.34.16% of human pregnancies last between 230 and 260 days.

Interpretation 2. Probability that a randomly chosen human pregnancy lasting between 230 days and 260 days is 0.3416.

36.

Interpretation 1. according to elena, 33.09% of cars have a miles/gallon higher than 26.

Interpretation 2. probability that a randomly chosen car has a miles/gallon higher than 26 is 0.3309

Interpretation 1. 11.07% chance that a randomly selected car has a miles/gallon between 18 and 21.

Interpretation 2. Probability that a randomly selected car has a miles/gallon between 18 and 21 is 0.1107

7.2

5.

  1. 0.0071
  2. 0.3336
  3. 0.9115

  4. 0.9998

  5. 0.9987
  6. 0.9441
  7. 0.0375

  8. 0.0009

9.

  1. 0.9586
  2. 0.2088
  3. 0.8479

11.

  1. 0.0456
  2. 0.0646
  3. 0.5203

13. -1.28

15. 0.68

17. -2.575 - 2.575

33. 40.62

35. 56.16

37.

  1. 15.87%
  2. 15.87%
  3. 47.72%
  4. unusual because it is only a 0.13% of it happening

39.

  1. 86.58%
  2. 1.32%
  3. 70.19%
  4. 12.30%
  5. 96th percentile
  6. 4th percentile

41.

  1. 40.13%
  2. 15.87%
  3. 75.9%
  4. 18.94%
  5. 9.51%
  6. yes, 0.4% of births are very preterm

43.

  1. 7.64%
  2. 3.24%
  3. 162 rods
  4. 11804 rods

45.

  1. 32.28%
  2. 42.86%
  3. yes

47.

  1. 20 days
  2. 19 - 23 days

56. SAT z-score is 1.019, ACT z-score is 0.96. The SAT was better

8.1

## Here is the syntax you can use to check the probabilities you look up are correct.

## Say you want to know the Pr(X < 5) and X is Normal with a mean of 12 and standard deviation 4

pnorm(5, mean = 12, sd = 4 )
## [1] 0.04005916

15.

  1. normal with mean of 80, spread of 2
  2. 6.68%
  3. 1.79%
  4. 79.69%

17.

  1. must be normally distributed. sampling distribution of mean must also be normal with mean of 64 and spread of 4.9
  2. 74.86%
  3. 40.52%

19.

  1. 35.2%
  2. Normal, mean 266, spread of 3.578
  3. 4.65%
  4. 0.4%
  5. unusual, because the probability is below 0.05.
  6. 0.9844

21.

  1. 0.3085
  2. 0.0418
  3. 0.0071
  4. as sample size increases, the probability decreases. this is because as n increases, the distribution (sigma over n) decreases
  5. not very effective because the probability is 0.1056
  6. 93.69 wpm

23.

  1. 0.5675
  2. 0.7291
  3. 0.8051
  4. 0.8531
  5. probability of earning increases as sample size increases

Here is the syntax you can use to check your answers. (Forward and Backward)

Say you want to know the \(Pr (\hat{P} < .35)\) and \(\hat{P} \sim \mathcal{N}(.4,.07)\)

pnorm(.35, mean = .4, sd = .07 )
## [1] 0.2375253

Here is the syntax you can use to check if a “Backward” calcuation is corect.

Say you know the probability to the left of \(\hat{p}\) = .04 and you want to know what the appropriate \(\hat{p}\) is. You also know that \(\hat{P} \sim \mathcal{N}(.4,.07)\)

qnorm(.05, mean = 12, sd = 4)
## [1] 5.420585

Section 8.2

11.

  1. normal, mean 0.8, stdev 0.046
  2. 0.1922
  3. 0.0047

12.

  1. normal, mean 0.65, stdev 0.034
  2. 0.1894
  3. 0.0375

13.

  1. normal, mean 0.35, stdev 0.015
  2. 0.004
  3. 0.0233

14.

  1. normal, mean 0.42, stdev 0.013
  2. 0.0102
  3. 0.0606

15.

  1. normal, mean 0.47, stdev 0.035
  2. 0.1977
  3. 0.0239. unusual because only 2% chance

16.

  1. normal, mean 0.82, stdev 0.35
  2. 0.2177
  3. 0.0344

17.

  1. normal, mean 0.39, stdev 0.022
  2. 0.3228
  3. 0.3198
  4. 0.0838. it is not unusual because it is larger than 0.05