7.1

31.

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

Interpretation 1. The proportion of plans that charge less than or equal to $44.00 is 0.1587.

Interpretation 2. The probability that a randomly selected cell phone plan costs less than $44.00 is 0.1587.

32.

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

Interpretation 1. The proportion of refrigerators that last more than 17 years is 0.1151.

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

33.

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

Interpretation 1. The proportion of full-term babies that weigh more than 4410 grams is 0.0228.

Interpretation 2.The probability that a randomly selected full-term baby weighs more than 4410 grams is 0.0228.

34.

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

Interpretation 1. The proportion of 10-year old males that are less than 46.5 inches tall is 0.0496.

Interpretation 2. The probability that a randomly selected 10-year old male is under 46.5 inches tall is 0.0496.

35.

Interpretation 1. The proportion of pregnancies that are longer than 280 days is 0.1908.

Interpretation 2. The probability that a randomly selected human pregnancy lasting longer than 280 days is 0.1908.

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

Interpretation 2. The probability that a randomly selected pregnancy will last between 230 and 260 days is 0.3416.

36.

Interpretation 1. The proportion of gas mileage that is greater than 26 miles per gallon is 0.3309.

Interpretation 2.The probability that a randomly selected gas mileage is more than 26 miles per gallon is 0.3309.

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

Interpretation 2. The probability that a randomly selected gas mileage is between 18 and 21 miles per gallon is 0.1107.

7.2

5.

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

7.

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

9.

  1. (0.9793) - (0.0207) = 0.9586.
  2. (0.5000) - (0.2912) = 0.2088.
  3. (0.9971) - (0.1492) = 0.8479.

11.

  1. to the left of -2: 0.0228 to the right of 2: 1 - 0.9772 = .0228 Total = 0.0456.
  2. to the left of -1.56: 0.0594 to the right of 2.56: 1 - 0.9948 = 0.0052 Total = 0.0646.
  3. to the left of -0.24: 0.4052 to the right of 1.20: 1 - 0.8849 = 0.1151 Total = 0.5203.

13. -1.28.

15. 0.68.

17. -2.57 and 2.57.

33. Z-score for 9th percentile: -1.34 9th percentile is a value of 40.62.

35. Z-score for 81st percentile: 0.88 81st percentile is a value of 56.16.

37.

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

  1. The probability that a randomly selected fertilized chicken egg hatches in less than 20 days is 0.1587.
  2. The probability that a randomly selected fertilized chicken egg takes over 22 days to hatch is also 0.1587.
  3. The probability that a randomly selected fertilized chicken egg will hatch between 19 and 21 days is 0.4772.
  4. Yes because there is only a 0.0013 probability that this could occur.

39.

  1. The probability that a randomly selected 18-ounce bag contains between 1000 and 1400 chocolate chips is 0.8660.
  2. The probability that a randomly selected 18-ounce bag contains less than 1000 chocolate chips is 0.0130.
  3. The proportion of 18-ounce bags that contain more than 1200 chocolate chips is 0.6985.
  4. The proportion of 18-ounce bags that contain less than 1125 chocolate chips is 0.1230.
  5. An 18-ounce bag containing 1475 chocolate chips is in the 96th percentile.
  6. An 18-ounce bag containing 1050 chocolate chips is in the 4th percentile.

41.

  1. The proportion of pregnancies that last more than 270 days is 0.4013.
  2. The proportion of pregnancies that last less than 250 days is 0.1587.
  3. The proportion of pregnancies that last between 240 and 280 days is 0.7590.
  4. The probability that a pregnancy lasts more than 280 days is 0.1894.
  5. The probability that a pregnancy lasts no more than 245 days is 0.0951.
  6. Yes, very preterm babies are unusual since only 0.0043 of the population experiences these births.

43.

  1. 0.0764 of rods are shorter than 24.9 cm.
  2. 0.0324 of all rods get discarded.
  3. The plant manager should expect to discard 162 of the 5,000 rods.
  4. The plant manager should manufacture 11,804 rods.