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April 17th, 2017, 05:43 PM   #1
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Finding the average day per week

Salaam

I have a simple word problem which I would like to solve in public.
I am sure you can agree with me.

If one trades labor for 30 days out of 53 days what would be the average days a week one trades?

Here is my answer.

wk 1 = 7 days of trade
wk 2 = 4 days of trade
wk 3 = 4 days of trade
wk 4 = 3 days of trade
wk 5 = 5 days of trade
wk 6 = 2 days of trade
wk 7 = 1 day of trade
wk 8 = 4 days of trade (counts as 1/2 week)

Step one.

FInd the Sum:

Sum = 7 + 4 + 4 + 3 + 5 + 2 + 1 + 4 = 30

Step two.

Divide 30 by 7.5 (the total number of weeks)

30 divided by 7.5 is 4, so the average is 4.
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April 17th, 2017, 05:56 PM   #2
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Better yet, can someone help me formulate this equation?
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April 18th, 2017, 10:02 AM   #3
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Quote:
Originally Posted by Nobel Bey View Post
Better yet, can someone help me formulate this equation?
the probability of having to labor on a given day is

$p=\dfrac{30}{53}$

the average days per week of labor is

$E[\text{days per week of labor}] = 7p = \dfrac{210}{53} \approx 3.96~day/week$
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April 18th, 2017, 04:31 PM   #4
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Salaam

Do you think one can also find the average days per week by dividing 53 days by 30 days of trade? Would that work or would I be finding weeks per day as opposed to days per week?
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April 18th, 2017, 05:31 PM   #5
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Quote:
Originally Posted by Nobel Bey View Post
Salaam

Do you think one can also find the average days per week by dividing 53 days by 30 days of trade? Would that work or would I be finding weeks per day as opposed to days per week?
no.

weeks have nothing to do with the probability a day is used for work.

weeks simply enter into it as a multiplication factor of 7 since there are 7 days in a week.
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April 19th, 2017, 05:18 AM   #6
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Thanks for your help romsek.
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