7.1

31.

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

Interpretation 1. 15.87% of the phone plans in the US are <$44.00 per month.

Interpretation 2. .1587 is the probability that a randomly selected phone plan in the US is <$44.00.

32.

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

Interpretation 1. 11.51% of refrigerators will live more than 17 years.

Interpretation 2. 0.1151 is the probability that a randomly selected refrigerator will last longer than 17 years.

33.

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

Interpretation 1. 2.28% of full term babies weigh more than 4410 grams.

Interpretation 2. .0228 is the probability that a randomly selected full term baby will weigh at least 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. .0496 is the probability that a randomly selected 10 year old males are not at least 46.5 inches tall.

35.

Interpretation 1. 19.08% is the proportion of human pregnancies that are more than 280.

Interpretation 2. .1908 is the probability that a randomly selected human pregnancy lasts longer than 280 days.

Interpretation 1. 34.16% is the proportion of human pregnancies that are 230 days or less.

Interpretation 2. .3416 is the probability that a randomly selected human pregnancy is 230 days or less.

36.

Interpretation 1. 33.09% is the proportion of times Elena’s Camry had over 26 MPG.

Interpretation 2. .3309 is the probability that Elena’s Camry has over 26 MPG.

Interpretation 1. 11.07% is the proportion of times that Elena’s Camry had 18MPG’s or less.

Interpretation 2. .1107 is the probability that Elena’s Camry had less than 18 MPG.

7.2

5.

  1. .0071
  2. .3336
  3. .9115
  4. .9998

7.

  1. .9987
  2. .9441
  3. .0375
  4. .0009

9.

  1. .9586
  2. .2088
  3. .8479

11.

  1. .0456
  2. .0646
  3. .5203

13. z=-1.28

15. z=0.67

17. z=2.575

33. 40.62

35. 56.16

37.

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

  1. p(x<20)=.1587
  2. p(x>22)=1-.8413=.1587
  3. p(19<x<21)=.5000-.0228=.4772
  4. Yes, it would be unusual for an egg to hatch in less than 18 days. Only 1/1000 eggs hatch in less than 18 days.

39.

  1. p(1000<x<1400)=.8790-.0132=.8658
  2. p(x<1000)=.0132
  3. p(x>1200)=1-.2981=.7019
  4. p(x<1125)=.1230 12.30%% is the proportion of 18oz Chips Ahoy cookies that contain less than 1125 chocolate chips
  5. p(x<1475)=.9645. An 18oz bag of Chips Ahoy cookies that have 1475 chocolate chips is the 96th percentile.
  6. p(x<1050)=.0359 An 18oz bag of Chips Ahoy cookies that contain 1050 chocolate chips is the 4th percentile.

41.

  1. 40.13%
  2. 15.87%
  3. 75.90%
  4. .1894
  5. .0951
  6. Yes, preterm by this questions standards aer unusual. Only 4/1000 births are “very preterm”.

43.

  1. 7.64% of rods.
  2. 3.24% of rods.
  3. 162/5000 steel rods the manager should expect to get rid of.
  4. 84.72% of the steel rods made will be in the 24.9cm through 25.1cm range. The manager should require 11804 rods to be made.