7.1

31.

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

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

Interpretation 2. The probability is 0.1587 that a randomly selected cell phone plan in the U.S. is less than $44 per month.

32.

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

Interpretation 1. 11.51% of refrigerators last more than 17 years.

Interpretation 2. The probability is 0.1151 that a randomly selected refrigerator lasts more than 17 years.

33.

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

Interpretation 1. 2.28% of all full term babies have a birth weight of more than 44100 grams

Interpretation 2. The probability is 0.0228 that the birth weight of a randomly chosen full term baby is more than 44100 grams

34.

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

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

Interpretation 2. The probability is 0.0496 that a radomly chosen 10-year old male is less than 46.5 inches tall.

35.

Interpretation 1. The proportion of human pregnancies that last more than 280 days is 0.1908

Interpretation 2. The probabilitiy that a randomly selected human pregnancy lasts more than 280 days is 0.1908

Interpretation 1. The proportion of pregnacies that last between 230 and 260 days is 0.3416

Interpretation 2. The probability that a randomly selected human pregnancy lasts betwwen 230 and 260 days is 0.3416

36.

Interpretation 1. The proportion of times Elena gets more than 26 miles per gallon in her gas tank is 0.3309.

Interpretation 2. The probability that a randomly selected gas tank will have more than 26 miles per gallon in it is .3309.

Interpretation 1. The proportion of gas tanks that get between 18 and 21 miles per gallon is 0.1107.

Interpretation 2. The probability that a randomly selected gas tank will have between 18 and 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 = 0.9987
  2. Area = 0.9441
  3. Area = 0.0375
  4. Area = 0.0009

9.

  1. Area = 0.9586
  2. Area = 0.2088
  3. Area = 0.8479

11.

  1. Area = 0.0456
  2. Area = 0.0646
  3. Area = 0.5203

13. z = -1.28

15. z = 0.67

17. z1 = -2.575, z2 = 2.575

33. x = 40.62 is at the 9th percentile

35. x = 56.16 is at the 81st percentile

37.

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

  1. P(X<20) = 0.1587. If 100 eggs are randomly chosen, we would expect 16 to incubate in less than 20 days.
  2. P(X>22) = 0.1587. If 100 eggs are randomly chosen, we would expect 16 to incubate in more than 22 days.
  3. P(19 less than or equal to X less than or equal to 21) = 0.4772. If 100 eggs are randomly chosen, we would expect 48 to incubate in between 19 and 21 days.
  4. Yes, P(X<18) = 0.0013. The model suggests that about 1 egg in 1000 incubates in less than 18 days.

39.

  1. P(1000 less than or equal to X les than or equal to 1400) = 0.8658
  2. P(X<1000) = 0.0132
  3. 0.7019 of the bags have more than 1200 chocolate chips
  4. 0.1230 of the bags have fewwer than 1125 chocolate chips
  5. A bag that contains 1475 chocolate chips is at the 96th percentile
  6. A bag that contains 1050 chocolate chips is at the 4th percentile

41.

  1. 0.4013 of pregnancies last more than 270 days
  2. 0.1587 of pregnancies last fewer than 250 days
  3. 0.7590 of pregnancies last between 240 and 280 days
  4. P(X>280) = 0.1894
  5. P(X less than or equal to 245) = 0.0951
  6. Yes, 0.0043 of births are very preterm. So about 4 births in 1000 births are preterm.

43.

  1. 0.0764 of the rods have a length of less than 24.9 cm
  2. 0.0324 of the rods will be discarded
  3. The plant manager expects to discard 162 of the 5000 rods manufactured.
  4. To meet the order, the plant manager should manufacture 11,804 rods.