quantitative methods: random sample to meas. oil changes

[dianharper]

In a small town of about 1200 people you have taken a random sample of 100 people. These 100 represent the total 1200 people. You are trying too ascertain the number of oil changes; so that, you can decide whether to open a Fast Lube location. The following table provides the results.

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   Number of    Weeks between
  respondents    oil changes
      30            8
      40           10
      20           12

Anyone not responding is assumed to never change his/her oil. For each group how many oil changes are made per week. Provide this information in the next table.

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    Number of  Average Oil changes per   Total oil
  respondents    week per respondent      changes
      30      
      40      
      20      

a) What are the total oil changes per week for these 100 people?

b) What are the total oil changes per week for the 1200 people in this town.

c) If an oil change is $30 how much will the town spend on oil changes per week?

d) Could you make a profit on a Quick Lube in this small town? Why? Why not?

[stapel_eliz]

To fill in the second table, divide to find the "fractional" oil change done "per week". For instance, if I get my oil changed every two weeks, then I get "half" an oil change "per week". If I get "half" an oil change and my neighbor gets "one-third" of an oil change, then the two of us together get 1/2 + 1/3 = 5/6 of an oil change per week.

a) What are the total oil changes per week for these 100 people?

Add the "total" column's values.

b) What are the total oil changes per week for the 1200 people in this town.

If the 100 are representative of the 1200, multiply the 100's number to get the 1200's number.

c) If an oil change is $30 how much will the town spend on oil changes per week?

Multiply the oil changes by the price per change.

d) Could you make a profit on a Quick Lube in this small town? Why? Why not?

Since you have no information about costs, there is no way to know whether this income is sufficient. Sorry!

If you get stuck on the parts that can be answered, please reply with a clear listing of your work and reasoning so far. Thank you!

Eliz.