7.1

31.

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

Interpretation 1. 15.87% of cell phone bills in the US are under $44

Interpretation 2. There is a probability of 0.1587 that a random cell phone bill is less than $44

32.

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

Interpretation 1. 89.49% of refrigerators live up to 17 years

Interpretation 2. There is a probability of .1151 that a randomly selected refrigerator lives over 17 years

33.

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

Interpretation 1. 2.28% of birth weights are at least 4410

Interpretation 2. A randomly selected birth weight has a probability of 0.0228 of being greater 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 .0496 probability of a randomly selected 10 year old boy being under 46.5 inches

35.

Interpretation 1. 19.08% of pregnancies are greater than 280 days

Interpretation 2. There is a .1908 probability of a pregnancy lasting longer than 280 days.

Interpretation 1. 34.16% of pregnancies last between 230 and 260 days

Interpretation 2. There is a .3416 probability of a random pregnancy lasting between 230 and 260 days

36.

Interpretation 1. The proportion of milage for cars that get at least 26 miles to the gallon is 33.09%

Interpretation 2. There is a .3309 probability of a cars milage being at least 26 miles per gallon

Interpretation 1. The proportion of cars that get between 18 and 21 miles to the gallon is 11.07%

Interpretation 2. There is a probability of .1107 of a randomly selected car getting 18 to 21 miles to the gallon

7.2

5.

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

7.

  1. 1- 0.0013= 0.9987
  2. 1- 0.0559= 0.9441
  3. 1- 0.9625= 0.0375
  4. 1- 0.9991= 0.0009

9.

  1. 0.9793-0.0207= 0.9586
  2. 0.5-.2912= 0.2088
  3. 0.9971-0.1492= 0.8479

11.

  1. 0.0228 + (1-0.9772) = 0.0228
  2. 0.0594 + (1-.09948) = 0.0646
  3. 0.4052 + (1-0.8849) = 0.5203

13. 1.003 = z=-1.28

15. 0.7486 = z=0.67

17. 0.0049=-2.58 and 0.0051=-2.57 (-2.58+-2.57)/2= z1=-2.575 0.9949=2.57 and 0.9951=2.58 (2.57+2.58)/2= z2=2.575

33. 0.0901= z=-1.34 x=50+(-1.34x7)=40.62

35. 0.8106= z=0.88 x=50+(0.88x7)=56.16

37.

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

  1. z=(20-21)/1=-1 z=-1.00 P(X<20)=0.1587
  2. z=(22-21)/1=1 z=1.00 P(x>22)=0.1587
  3. z=(19-21)/1=-2.00 z=-2.00 P(x<19)=0.0228 P(x<21)=0.500 0.500-0.0228=0.4772
  4. z=(18-21)/1=-3.00 z=-3.00 P(x<18)=0.0013 It is very unlikely for an egg to hatch in under 18 days. The probability is about 1 in every 1000 eggs.

39.

  1. (1400-1262)/118=1.17 z1=1.17=0.8790 (1000-1262)/118=-2.22 z2=-2.22=0.0132 0.8790-0.0132=0.8658
  2. P(x<1000)=0.0132
  3. (1200-1262)/118=-62 P(x>1200)=-0.53 z=-0.53=0.2981 1-0.2981=0.7019 The proportion of bags of cookies that contain more than 1200 chips is 70.19%
  4. (1125-1262)/118=1.16 z=-1.16 P(x<1125)=0.1230 Proportion of bags with less than 1125 chips is 12.3%
  5. (1475-1262)/118=1.81 z=1.81=0.9649 A bag containing more than 1475 chips is in the 96th percentile.
  6. (1050-1262)/118=-1.80 z=1.80=0.0359 A bag containing less than 1050 chips is in th 4th percentile.

41.

  1. (270-266)/16=0.25 z=0.25=0.5987 1-P(x<270)=0.4013
  2. (250-266)/16=1.00 z=1.00=.1587 P(x<250)=0.1587
  3. (240-266)/16=1.63 z=1.63 P(x<240)=0.0516 (280-266)/16=0.88 P(x<280)=0.8106 0.8106-0.0516=0.7590
  4. 1-P(x>280)=0.1894
  5. (245-266)/16=-1.31 z=-1.31 P(x<245)=0.0951
  6. (224-266)/16=-2.63 z=-2.63 P(x<224)=0.0043 Very preterm babies are extremely rare, about four in every 1000 births.

43.

  1. (24.9-25)/0.07=-1.43 z=-1.43 P(x<24.9)=0.0764 Proportion of rods with a diameter of less than 24.9cm is 7.64%
  2. (24.85-25)/0.07=-2.14 P(x<24.85)=0.0162 (25.15-25)/0.07=2.14 1-P(x>25.15)=0.9838 P(24.85x) 2(0.0162)=0.0324 Proportion discarded will be 3.24%
  3. 5000xP(24.85>x<25.15)=162 Managershould expect to discard 162 rods
  4. (24.9-25)/0.07=-1.43 P(x<24.90)=0.0764 (25.1-25)/0.07=1.43 P(x<25.1)=0.9236 0.9236-0.0764=0.8472 84.72% of rods will be within 24.9cm and 25.1cm. 10,000x0.8472=8,472 10,000-8,472=1528 The manufacturer should produce 11,528 rods because roughly 1,528 will not be within desired diameter range.