7.1

31.

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

Interpretation 1. 15.87% of the cell phone plans are less than $44 per month.

Interpretation 2. When randomly selected a cell phone plan, the probability that the plan is less than $44 is 0.1587.

32.

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

Interpretation 1. 11.51% of all refrigerators are kept more than 17 years.

Interpretation 2. When randomly selected refrigerator, the probability of a more than 17 years old regrigerator is 0.1151.

33.

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

Interpretation 1. 2.28% of all full-term babies have birth weights that are at least 4410 g.

Interpretation 2.When randomly chose a full-term baby, the prabability birth weight that is at least 4410 g is 0.0228.

34.

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

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

Interpretation 2. When randomly selected a 10-year-old male, the probability that he is less than 46.5 inches tall is 0.0496.

35.

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

Interpretation 2. When randomly selected human pregnancy day, the probability of more than 280 days is 0.1908.

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

Interpretation 2. When randomly selected human pregnancy day, the probability between 230-260 days is 0.3416.

36.

Interpretation 1. 33.09% of times Elena gets more than 26 miles per gallon.

Interpretation 2. When randomly selected the fill-up yields, the probability times that Elena gets more than 26 miles per gallon is 0.3309.

Interpretation 1. 11.07% of times Elena gets between 18-21 miles per gallon.

Interpretation 2. When randomly selected the fill-up yields, the probability of times that between 18-21 miles per gallon is 0.1107.

7.2

5.

  1. area=0.0071.
  2. area=0.3336.
  3. area=0.9115.
  4. area=0.9998.

7.

  1. area:1-0.0013=0.9987.
  2. area:1-0.0559=0.9441.
  3. area:1-0.9625=0.0375.
  4. area:1-0.9991=0.0009.

9.

  1. area:0.9793-0.0207=0.9586.
  2. area:0.5-0.2912=0.2088.
  3. area:0.9971-0.1492=0.8479.

11.

  1. area:0.0228+0.0228=0.0456.
  2. area:0.0594+0.0052=0.0646.
  3. area:0.4052+0.1151=0.5203.

13. z=-1.28.

15. z=0.67.

17. z1=-2.575, z2=2.575.

33. X=50+(-1.34)x7=40.62.

35. X=50+0.88x7=56.16.

37.

shadenorm(mu = 21, sig = 1.0, below = -1000, col = "blue", dens=200)

  1. z=-1, so the probability is 0.1587.
  2. z=1, so probability=1-0.8413=0.1587.
  3. z1=-2, z2=0, probability=0.5000-0.0228=0.4772.
  4. z=-3, probability is 0.0013, so yes, it would be unusual for an egg to hatch in less than 18 days, because in 1000 egg, about 1 would hatches in less than 18 days.

39.

  1. z1=-2.22, z2=1.17, probability=0.8790-0.0132=0.8658.
  2. z=-2.22, so probability is 0.0132.
  3. z=-0.53, probability=1-0.2981=0.7019=70.19%.
  4. z=-1.16, probability=0.1230=12.30%.
  5. z=1.81, probability=0.9649, so about 96th percentile contains 1475 chocolate chips.
  6. z=-1.80, probability=0.0359, so about 4th percentile contains 1050 chocolate chips.

41.

  1. z=0.25, probability=1-0.5987=0.4013=40.13%.
  2. z=-1, probability=0.1587=15.87%.
  3. z1=-1.63, z2=0.88, probability=0.8106-0.0516=0.7590=75.90%.
  4. z=0.88, probability=1-0.8106=0.1894.
  5. z=-1.31, so probability=0.0951.
  6. z=-2.63, probability=0.0043, so yes, the “very preterm” babies are unusual.

43.

  1. z=-1.43, probability=0.0764=7.64%.
  2. z1=-2.14, z2=2.14, probability=2x0.0162=0.0324=3.24%.
  3. 5000x0.0324=162.
  4. z1=-1.43, z2=1.43, probability=0.9236-0.0764=0.8472, 0.8472x=10000, x=11804 rods.