7.1

31.

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

Interpretation 1. 84% or people pay more than 44 dollars per month for their cell phone plans.

Interpretation 2. 1,587 out of every 10,000 pay 528 or less per year for their cell phone plans.

32.

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

Interpretation 1. 11.5 percent of refrigerators last more than 17 years.

Interpretation 2. 38.5percent of refrigerators last more than 14 years, but less than 17 years.

33.

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

Interpretation 1. It is unlikely than a baby will be born weighing more than 4410 because the probablitiy is less than 0.05

Interpretation 2.98 percent of babies weigh less than 4410 at birth.

34.

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

Interpretation 1. 45 percent of ten year old boys are between 46.5 inches and 55.9 inches tall

Interpretation 2. 95 percent of ten year old boys are shorter than 65.3 inches tall.

35.

Interpretation 1. 19 percent or pregnancies are longer than 280 days

Interpretation 2. 31 percent of pregnancies are between 266 and 280 days.

Interpretation 1.65.84 percent of pregnancies are not between 230 and 260 days.

Interpretation 2. the change that a pregnancie will last between 230 and 260 days is 34 out of a hundred.

36.

Interpretation 1. Under certain conditions, 33.09 percent of the time, Elenas car will drive more efficiently than 26 miles per gallon.

Interpretation 2. 66.91 percent of the time, Elenas car drives less efficiently than 26 miles per gallon.

Interpretation 1. eleven percent of the time, Elena will only be able to drive 18~21 miles per gallon.

Interpretation 2. Elena will have gotten 18 to 21 miles per gallon 4 or 5 times during her experiemnt.

7.2

5.

  1. .0071
  2. .3336
  3. .9115
  4. .9998

7.

  1. .9987
  2. .9441
  3. .0375
  4. .0009

9.

  1. .9586
  2. .2088
  3. .8479

11.

  1. .0456
  2. .0646
  3. .5203

13. -1.28

15. .068

17. -3.3 and 2.57

33. -5.85

35. 4.43

37.

  1. .16 (b).16
  2. .4985
  3. because there is only a 0.15 percent chance

39.

  1. .8658
  2. .0132
  3. .6985
  4. .1230
  5. 96.41
  6. 3.67

41.

(a).4031 (b) .1587 (c).7552 (d) .1922 (e) .0951 (f) yes

43.

  1. .0764
  2. .0324
  3. 162
  4. 10324

45.

  1. I don’t understand this set of questions.

47.

  1. 20.05 or less
  2. (19,23)

56. the SAT because z score for sat is .8461, and z score for ACT is .8315

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. Xbar is normal with (80,14)
  2. .0668
  3. .0179
  4. .1923

17.

  1. X~N(64,17)
  2. .6724
  3. .7554

19.

  1. .3520
  2. X~N(266, 16/root20)
  3. .0465
  4. .0040
  5. unusual, population may not be 266
  6. .9844

21.

  1. .3085
  2. .0418
  3. .0071
  4. increase in sample size increases probablility.
  5. .1065
  6. (X-90)/(10/root20)

23.

  1. .4325
  2. .7257
  3. .1977
  4. .1492
  5. as the horizon increases, the chances get smaller.

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. Phat~ 10,000(.8, .046)
  2. .8078
  3. .0047

12.

  1. P hat~ 25,000(.65, .0337)
  2. .8133
  3. .0375

13.

  1. X~1,000,000 (.35, .015)
  2. .9961
  3. .0228

14.

  1. X~ 1,500,000 (.42,.0129)
  2. .9898
  3. .0606

15.

  1. X~ all americans (.47, .035)
  2. .8051
  3. yes because p is less than .05

16.

  1. X~ Americans (.82, .038)
  2. .7852
  3. yes because p is less than .03

17.

  1. X~ adult americans (.39, .0218)
  2. .3264
  3. .3234
  4. Yes.