7.1

31.

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

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

Interpretation 2. There is a 0.1587 probability that a randomly chosen phone plan in the United States 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 for more than 17 years.

Interpretation 2. There is a 0.1151 probability that a randomly selected refrigerator will live for more than 17 years.

33.

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

Interpretation 1. 2.28% of full-term babies have a birth weight of more than 4410 grams.

Interpretation 2.There is a 0.0228 probability that the birth weight of a randomly selected full-term baby will be more than 4410 grams.

34.

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

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

Interpretation 2. There is a 0.0496 probability that the height of a randomly selected 10 year old male will be less than 46.5 inches tall.

35.

Interpretation 1. There is a 0.1908 probability that a randomly selected human pregnancy will last more than 280 days.

Interpretation 2. The proportion of human pregnancies that last more than 280 days is 0.1908.

Interpretation 1.There is a 0.3416 probability that a randomly selected human pregnancy will last between 230 and 260 days.

Interpretation 2. The proportion of human pregnancies that last between 230 and 260 days is 0.3416.

36.

Interpretation 1. There is a 0.3309 probability that a randomly selected time when Elena fills up her gas tank the miles per gallon will be over 26.

Interpretation 2. The proportion of times that her gas tank will work at an efficiency of over 26 miles per gallon is 0.3309.

Interpretation 1. The is a 0.1107 probability that her tank will work at an efficiency between 18 and 21 miles per gallon.

Interpretation 2. The proportion of times that her gas tank will work at an efficiency 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 the 81st percentile.

37.

  1. P(X<20) = 0.1587.
  2. P(X>22) = 0.1587.
  3. P(19<X<21) = 0.4772.
  4. Yes; P(X<18) = 0.0013. Approximately 1 out of 1000 eggs hatch in less than 18 days.

39.

  1. P(1000<X<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 fewer than 1125 chocolate chips.
  5. A bag that has 1475 chocolate chips is in the 96th percentile.
  6. A bag that has 1050 chocolate chips is in the 4th percentile.

41.

  1. 0.4013 of the pregnancies last more that 270 days.
  2. 0.1587 of the pregnancies lasts for less 250 days .
  3. 0.7590 of pregnancies last between 240 and 280 days.
  4. P(X>280) = 0.1894.
  5. P(X<245) = 0.0951.
  6. Yes; 0.0043 of the births are very preterm. Approximately 4 out of 1000 births are very preterm.

43.

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

45.

  1. P(X>5) = 0.3228.
  2. P(X<-2) = 0.4286.
  3. “The margin of victory relative to the spread has a mean of 0 points” means that, relative to the spread, the favored team has an equal likelihood to win or lose. Yes, the spreads are accurate because the mean is 0.

47.

  1. The 17th percentile for incubation time is 20 days.
  2. The incubation times that make up the middle 95% of fertilized chicken eggs is between 19 and 23 days.

56. The SAT score was the better score because it landed in the 95 percentile, thus being greater than one standard deviation from the mean. In contrast, the ACT score landed in the 68th percentile, being less than one standard deviation from the mean.