7.1

31.

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

Interpretation 1. If the area of the shaded region is 0.1587, that means that 15.87% of the distribution have a phone plan that costs $44 or less. Interpretation 2. If a plan was randomly selected out of the entire population, the probability it will cost $44 or less is 0.1587.

32.

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

Interpretation 1. If the area of the shaded region is 0.1151, that means that 11.51% of the refrigerators tested have a lifespan of 17 years or greater.

Interpretation 2. If a refrigerator was randomly selected from the entire sample, the probability the refrigerator will have a lifespan of 17 years or greater is 0.1151.

33.

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

Interpretation 1. If the area under the shaded region is 0.0228, that means that 2.28% of the babies tested have a weight of 4410 grams of higher.

Interpretation 2. If a baby was randomly selected from the entire sample, the probability it will weight 4410 grams or higher is 0.0228.

34.

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

Interpretation 1. If the area under the shaded region is 0.0496, that means that 4.96% of the males tested have a height of 46.5 inches or lower.

Interpretation 2. If a male was randomly selected from the entire sample, the probility he will be 46.5 inches or lower is 0.0496.

35.

Interpretation 1. 19.08% of the participants had a pregancy that lasted 280 days or more.

Interpretation 2. A randomly selected pregancy out of the sample has a 0.1908 probability that it will be 280 days or more. (b)

Interpretation 1.34.16% of the pregancies lasted between 230 and 20 days.

Interpretation 2. A randomly selected pregancy out of the sample has a 0.3416 probability that it will last between 230 and 260 days.

36.

Interpretation 1. 33.09% of the trips she took were 26 mpg or greater.

Interpretation 2. If she were to randomly select one of the trips, there is a 0.3309 probability that the trip she selects averaged 26 mpg or more.

Interpretation 1. 11.07% of the trips she took were between 18 and 21 mpg.

Interpretation 2. If she were to randomly select one of the trips, there is a 0.1107 probability that the trip she selects averaged between 18 and 21 mpg.

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. 0.9586
  2. 0.2088
  3. 0.8479

11.

  1. 0.0456
  2. 0.0646
  3. 0.5203

13.-1.28

15. 0.67

17. -2.575 , 2.575

33. 40.62

35. 56.16

37.

  1. 0.1587
  2. 0.1587
  3. 0.4772
  4. 0.0013

39.

  1. 0.8658
  2. 0.0132
  3. 0.7019
  4. 0.1230
  5. 96th
  6. 4th

41.

  1. 0.4013
  2. 0.1587
  3. 0.7590
  4. 0.1894 (e)0.0951
  5. Yes. 0.0043 probability of births are preterm, which is a very small amount.

43.

  1. 0.0764
  2. 0.0324
  3. 162 rods will be discarded
  4. 11,804 rods should be made.

45.

  1. 0.3228
  2. 0.4286
  3. The favored team has an equal chance of winning or losing. They are accurate as the mean is 0.

47.

  1. 17th percentile
  2. 19-23 days is the middle 95%

56. You scored better on the SAT, as the difference between the mean and your score is more than one standard deviation greater than the average. Whereas in the ACT, you scored less than one standard deviation greater than average.