7.1

31.

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

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

Interpretation 2. The probability is 0.1587 that a randomly selected cell phone plan in the US is less than 44$ per month. 32.

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

Interpretation 1. 11.51% of the refrigerators are used for 17 or more years.

Interpretation 2. The probability is 0.1151 that a randomly selected refrigerator will be used for 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 4410 grams.

Interpretation 2. The probability is 0.0228 that the birth weight of a randomly chosen full-term baby is more than 4410 grams.

34.

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

Interpretation 1.The proportion of 10-year old males who are shorter than 46.5 inches is 0.0496.

Interpretation 2. The probability is 0.0496 that a randomly chosen 10-year old male is shorter than 46.5 inches.

35.

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

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

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

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

36.

Interpretation 1. The proportion of times Elena fills up more than 26 miles per gallon for each fill-up is 0.3309.

Interpretation 2. The probability that a fill up chosen randomly yields more than 26 miles per gallon is 0.3309.

Interpretation 1. The proportion of times Elena fills up between 18 and 21 miles per gallon is 0.1107.

Interpretation 2. The probability that a fill up chosen randomly yields 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 selected, we would expect 16 to incubate in less than 20 days.
  2. P(X>22) = 0.1587. If 100 eggs are randomly selected, we would expect 16 to incubate in more than 22 days.
  3. P(19??? X ???21) = 0.4772. If 100 eggs are randomly selected, 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. 0.8658.
  2. P(X<18) = 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 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. 0.1894
  5. 0.0951
  6. Yes, 0.0043 of births, therefore about 4 in 1000 births are very preterm.

43.

  1. 0.0764 of the rods have a lenght of less than 24.9cm
  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

45.

  1. The favored team is equally likely to win or lose relative to the spread. Yes, a mean of 0 implies the spreads are accurate
  2. 0.3228
  3. 0.4286

47.

  1. The 17th percentile for incubation time is 20 days.
  2. From 19 to 23 days make up the middle 95% of the incubation times of the eggs.

56. This means you scored better on the SAT because the percentile for SAT is 85% while the percentile for ACT is 83%.