7.1

31.

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

Interpretation 1. 15.87% of people have monthly charges less than $44

Interpretation 2. Probability of a randomly selected plan to be under $44 = 0.1587; Z score = -1

32.

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

Interpretation 1. 88.49% of the refrigrators have a life last less than or equal to 17 years

Interpretation 2. probability of a randomly selected refrigrator to have a life more than 17 years = 0.1151; Zscore = 1.2

33.

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

Interpretation 1. 97.72% of the babies have weight less than 4400.

Interpretation 2. probability of a randomly selected baby to have weight more than or equal to 4400 = 0.0228; Z score = 2

34.

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

Interpretation 1. 4.96% of 10 year olds have height less than 46.5 inches

Interpretation 2. probability of a randomly selected 10 year old to have height less than 46.5 inches = 0.0496; z score= 1.649

35.

Interpretation 1. 19.08% of the human pregnancy gestation period lasts longer than or equal to 280 days

Interpretation 2. probability of a randomly selected gestation period to last more than 280 days = 0.1908

Interpretation 1. 34.16% of gestation pregnancy period is between 230- 260 days

Interpretation 2. probability of gestation period to be between 230 - 260 days = 0.3416. 36.

Interpretation 1. 33.09% times mileage is greater than 26miles/gallon Interpretation 2. probability of a randomly selected mileage to be greater than 26 is 0.3309.

Interpretation 1. 11.07% times milleage will be between 18 and 21

Interpretation 2. probability of a randomly selected mileage to be between 18 and 21 = 0.1107

7.2

5.

  1. 0.0072
  2. 0.3336
  3. 0.9115
  4. 0.9998

7.

  1. 0.9987
  2. 0.9441
  3. 0.0375
  4. 0.0009

9.

  1. 0.9586
  2. 0.2088
  3. 0.8479

11.

  1. total area= 0.0456; to the left: 0.0228; to the right: 0.0228
  2. total area= 0.0646; to the left:0.0594; to the right: 0.0052
  3. total area= 0.5202; to the left: 0.4052; to the rifht: 0.1151

13. Z score = - 1.28

15. Z score = 0.67

17. Z score = -2.58/-2.57 && Z score = 2.58/2.57

33. 40.62

35. 56.16

37.

  2. .1587
  3. .1587
  4. .4772

39.

  1. 0.8658
  2. 0.0132
  3. 0.7019 or 70.19%
  4. 0.1230 or 12.30%
  5. 96th percentile
  6. 4th percentile

41.

  1. 40.13 %
  2. 15.87% or 0.1587
  3. 0.7590 or 75.90%
  4. 0.1894
  5. 0.0951
  6. YES they are unusual

43.

  1. 0.0764 or 7.06%
  2. 0.0324 or 3.24%
  3. 162 of the 5000 steel rods should be discared (expectation)
  4. 11,804 rods should be produced in order for them to be between 24.9 or 25.1 cm

45.

  1. Yes the probability is 50/50; spreads are accurate
  2. 0.3228
  3. 0.4286

47.

  1. z score- -0.95 =20 days
  2. 95% incubation is between 19-23 days

56. The SAT score was better than the ACT score, since sat Z score= 1.019 whereas ACT Z score = 0.88, thus the area to the left of the curve would be higher for the sat score than the act score.