# Thread: What are the odds? (2000)

1. ## What are the odds? (2000)

Question: Bulk shortening tank holds 1000 gallons of shortening. Deliveries are two times per month. Delivery #1is 577.4 lbs, 14 days later, delivery #2 is 577.4 lbs.

Is the probability of this happening 1 in 10000, or something else?

2. ## Re: What are the odds? (2000)

I'd say the numbers were filled in prior to delivery. On the other hand, if the numbers are accurate, this could be a sign! Played the Texas lottery lately??

3. ## Re: What are the odds? (2000)

What is the range and std dev of typical shipments? If the range is from 0 to 8000 lbs will yield different odds than if the numbers range from 560-590 since in the latter case the 5 is immaterial, since it is ALWAYS a 5 in the first place.
Steve

4. ## Re: What are the odds? (2000)

Coming from you Ricky, I thought you would say "slim to none"! Got some of the <img src=/S/notmyfault.gif border=0 alt=notmyfault width=15 height=15> stuff from the "national" oil company.

~~~ Jeez, who put the "hugs" smilie in the smilies panel?~~~

Computer generated delivery slip with signature. On a separate thought from the probability question, also had two deliveries for another store, 12th and 26th of the month, where the slip shows the same company delivered 1000.8 lbs and 1001.0 lbs into a 960 lb tank! Wonder what the probability of that is???!!! Where is the food cost judge!?

5. ## Re: What are the odds? (2000)

Re: "Bulk shortening tank holds 1000 gallons of shortening. Deliveries are two times per month. Delivery #1is 577.4 lbs, 14 days later, delivery #2 is 577.4 lbs".
How many lbs of shortening to the gallon?

As for "same company delivered 1000.8 lbs and 1001.0 lbs into a 960 lb tank", the capacity of the tank is probably volume-based, not weight-based, so it's quite possible for a high-density product to weigh more than the rated capacity of the tank. Even if that were not so in this case, you'd probably find the rated capacity is a bit on the conservative side, possibly by as much as 5%.

6. ## Re: What are the odds? (2000)

My mistake, the tank holds 1000 lbs of shortening not gallons

Per vendor specs, the tank has a capacity of 960 lbs and shortening is delivered by the pound. It is dispensed through a hose, and although the amount delivered may be charged by the lb, surely the volume delivered through the hose must be calculated via some method to arrive at a correct poundage.

The above, coupled with the fact that two deliveries within the same month for the same store amounted to the same weight based charge would make me surmise that something funny is happening.

7. ## Re: What are the odds? (2000)

You have to keep in mind that the tank holds a fixed volume, not a fixed weight. What weight you can put into that volume depends entirely on the density of what it's being filled with. When its full of air, it won't weigh much at all compared to when its full of shortening.

As I said in my last post, the rated capacity is probably conservative. This is usually done to allow for post-delivery expansion due to temperature change. I imagine that you've seen what happens when people fill their fuel tanks on a cold morning, then leave their cars out in the hot sun - fuel soon starts overflowing. All the while, though, the fuel tank has held the same volume of fuel. But if you were to weigh the fuel tank just after it had been filled, you might well find it was heavier than it's nominal capacity would have indicated. Later in the day, the same (full) fuel tank might weigh less than it's nominal capacity would indicate.

Given that the shortening is piped in, it is almost certainly measured by volumem, as you suggest. That volume can be converted to weight (eg 1gal = 10lb, or 1l = 1kg). Added to that, some companies apply a temperature correction factor, so that calculations for deliveries in cold weather are adjusted (upwards) to take account of thermal contraction. Petrol companies in Australia do just that when charging service stations for the fuel the companies supply.

I agree that two consecutive deliveries for the same weight, down to 0.1lb, is unlikely. I also think it quite unlikely that volume deliveries would actually be measured to 0.1lb accuracy. These might both might be explained by the delivery equipment being calibrated for kg, but charges being made in lb (262kg:577.4lb, 454kg:1000.6-1001lb (depending on who's doing the conversion)). Two independent and consecutive deliveries of 262kg, though still unlikely, are far more probable than two of 577.4lb.

All in all, though, you should be able to validate (or invalidate) the bills if you know how much shortening should have been used over the period in question. Consistency with charges for equivalent periods would also be a useful guide.

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