7.1

31.

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

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

Interpretation 2. The probability is 0.1587 that a randomly selected cell phone plan in the US is less than $44.00 per month.

32.

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

Interpretation 1. 11.51% of refrigerators last more than 17 years.

Interpretation 2. The probability is 0.1151 that a randomly selected refrigerator has a lifespan of 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 a randomly picked 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. 4.96% of 10-year old males have a height of less than 46.5 inches.

Interpretation 2. The probability is 0.0496 that a randomly picked 10-year old male is less 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 number of miles per gallon per fill up that is more than 26 miles per gallon is 0.3309.

Interpretation 2. The probability that a randomly selected fill up results in more than 26 miles per gallon is 0.3309.

Interpretation 1. The proportion of number of miles per gallon per fill up is between 18 and 21 miles per gallon is 0.1107.

Interpretation 2. The probability that a randomly selected fill up results 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. z= -2.572; z= 2.572

33. x= 40.62; 9th percentile

35. x= 56.16; 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. About 1 egg in 1000 hatches 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 less 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 less than 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 births are very preterm. About 4 births in 1000 births are very preterm.

43.

  1. 0.0764 of the rods have a length of less than 24.9 cm.
  2. 0.0324 of rods will be discarded.
  3. The plant manager expects to discard 162 of the 5000 rods made.
  4. To meet the order, the plant manager should make 11,804 rods.

45.

  1. P(X >= 5)= 0.3228
  2. P(X<= -2)= 0.4286
  3. The favored team is equally likely to win of lose relative to the spread. Yes; a mean of 0 implies the spreads are accurate.

47.

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

56. I did better on the SAT because I scored a little more than 1 standard deviation away from the mean. Compared to the ACT, where I scored less than 1 standard deviation away from the mean.