Problem 1 (40 points) Steel wide flange beams (shown to the right) are used in constructing the frames of modern buildings. Beams can be purchased from US, Japanese, or Chinese sourses.100 10" X 4" X 20' (nominal weight = 12 pounds per linear foot) beams are purchased from each country and 12 randomly selected beams from each country are weighed. These sample weights are shown in the table below:

Determine the following:


  1. The mean and standard deviation for each sample.
  2. Calculate the coefficient of variation for each sample.
  3. 20 foot beams should weigh 240 lbs. Calculate the probability of getting a beam that weighs exactly 240 lbs or less from each country.
  4. Which country seems to have the best "quality control"? Explain why.

Problem 2 (20 Points) The frequency distribution table shown to the right describes the speeds of drivers ticket by the Canon City Police Department during December 2008. These drivers were driving down Highway 50 vicinity of Safeway where the posted speed limit is 30 miles per hour.

  1. Calculate the standard deviation of the sample data summarized in the frequency distribution table.
  2. Can you make any generalized statements about the driving population passing by Safeway on Highway 50? EXPLAIN WHY OR WHY NOT.

Problem 3 (10 Points) Explain Chebyshev's Theorem. Use an example to demonstrate your understanding.

racing times in seconds.

Problem 4 (30 Points) You wish to compare the relative racing statistics races for two racing quarter horses. A randomly selected sample of each horse's last 100 races (in seconds) is shown to the right. One horse (Crazy Legs) runs exclusively in 5 furlong races while the other horse (Dead Weight) runs exclusively in 8 furlong races [one furlong = 220 yards].

Answer the following:


  1. If Cray Legs ran a 5 furlong race in 65 seconds, compute what would be an equivalent time for Dead Weight in an 8 furlong race.
  2. Compute the probability Dead Weight will run a race in more than 100 seconds but less than 105 seconds.
  3. What would be an "unusual value" for Crazy Leg to run a race in? Explain why.
  4. A race of 104 seconds for Dead Weight would be in what quartile?

Bonus (10 Points).

What founding father of the USA (and 3rd President) said:


"What all agree upon is probably right; what no two agree in most probably is wrong."