Solutions — Exercises I / 4.3
  1.  
    1. 400 < x < 600,   300 < x < 700,   and   200 < x < 800
    2. P(400 < x < 600)  ~  68.26%
      P(300 < x < 700)  ~  95.44%
      P(200 < x < 800)  ~  99.74%

    3. Bell-curve for Exercise #1
  2.  
    1. 15.8 < x < 16.2,   15.6 < x < 16.4,   and   15.4 < x < 16.6
    2. P(15.8 < x < 16.2)  ~  68.26%
      P(15.6 < x < 16.4)  ~  95.44%
      P(15.4 < x < 16.6)  ~  99.74%

    3. Bell-curve for Exercise #2
  3. a  50%           b.  Approx. 84%           c.  Approx. 16%

  4. a  50%           b.  Approx. 0.1%          c.  Approx. 0.1%

  5. Approx. 16 people

  6. Approx. 2 years

  7. 35,000 miles

  8. 29,000 miles

  9. 90 (or above)

  10. A:  90 or above
    B:  78-89
    C:  53-77
    D:  41-52
    F:  40 or below

  11. A:  97 or above
    B:  81-96
    C:  50-80
    D:  35-49
    F:  34 or below

  12. Yes, the assertion that less than 1% of the CD-players will fail before the warranty
    period expires is statistically valid... 
    For a typical user, the # hours of operation in a 30 month period will be:
    3 hr/d  ×  365.25 d/yr  ×  2.5 yr  ~  2739 hr

    Bell-curve for Exercise #12
    P(t < 2739 hr)   <  P(t < 2750 hr) 
      =  P(t < 3500 hr)  -  P(2750 hr < t < 3500 hr)
      ~  50% - (2.15% + 13.59% + 34.13%)
      =  50% - 49.87% 
      =  0.13% 
      <  1%