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Chapter 7 HW
Tom Linton, March 11, 2000
  1. Suppose that individual 12-ounce bottles of a certain beverage have volumes that are normally distributed with a mean volume of 11.8 ounces and a standard deviation of 0.11 ounces (not every bottle has exactly 12 ounces in it).
    1. How likely is it to find one bottle with more than 12 ounces in it?
    2. How likely is it to find a six-pack with the average volume per bottle exceeding 12 ounces?
    3. How likely is it that a 12-pack has S < 0.093 ounces, for its standard deviation?
    4. Here is a six-pack with an above average standard deviation:


      5. six-pack one
      bottle 1 2 3 4 5 6
      ounces 11.88 11.60 11.90 11.76 11.63 11.98

      and a six-pack with a below average standard deviation:
       

      six-pack two
      bottle 1 2 3 4 5 6
      ounces 11.81 11.65 11.74 11.85 11.75 11.68
      How likely is that two other samples of size 6 have a ratio larger than (S for six-pack one) / (S for six-pack two)?
  2. Eggs have weights that are normally distributed with a mean of 1.5 ounces and a standard deviation of 0.35 ounces. How likely is it that a carton (of 12 eggs) weighs a total of 19.8 ounces (or more)?
  3. When using a full swing with his driver (the club that goes the farthest), Tiger Woods hits his drives X yards, where X is normally distributed with a mean of 312 yards and unknown standard deviation. On the practice tee at Pebble Beach, Boris Batenoff hands Tiger a new driver that Boris claims will add yardarge to Tiger's drives. Upon practicing with this new club, Tiger decides to use the club for all of his drives that day. Tiger uses the new driver on 13 of the 18 holes. His yardages for these 13 drives are given below.
Hole 1 2 4 5 7 9 10 11 13 14 16 17 18
Yardage 352 315 332 330 350 320 323 331 267 360 342 307 305
    1. What was the average yardage of Tiger's drives with the new club?
    2. How large is the standard deviation of Tiger's 13 drives?
    3. How likely is it that Tiger would hit 13 drives, with an average greater than or equal to the one above, if the new club had the same mean yardage as his old club?
    4. Do you think that the new club really adds yardage to Tiger's drives, or are the 13 drives listed likely to occur just by good fortune on a day at the course?
    5. Re-calculate the answer to part (c) under the assumption that the old club yardages had the sample standard deviation, S, as their standard deviation (i.e. assume s = S).