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Parts at a factory are packed into shipping containers. The weights o

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Parts at a factory are packed into shipping containers. The weights o [#permalink] New post   31 Jul 2022, 23:39
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Parts at a factory are packed into shipping containers. The weights of the boxes are approximately normally distributed with an average of 50 pounds and a standard deviation of 7 pounds.


Quantity A
Quantity B
The approximate percentage of boxes that weigh less than 43 pounds
The approximate percentage of boxes that weigh more than 64 pounds



A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given

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Re: Parts at a factory are packed into shipping containers. The weights o [#permalink] New post   08 Aug 2022, 05:04
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Re: Parts at a factory are packed into shipping containers. The weights o [#permalink] New post   08 Aug 2022, 14:49
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Parts at a factory are packed into shipping containers. The weights of the boxes are approximately normally distributed with an average of 50 pounds and a standard deviation of 7 pounds.


Quantity A
Quantity B
The approximate percentage of boxes that weigh less than 43 pounds
The approximate percentage of boxes that weigh more than 64 pounds



A. Quantity A is greater
B. Quantity B is greater
C. The two quantities are equal
D. The relationship cannot be determined from the information given



Quantity A:
43 pounds is one standard deviation below the mean. Following the image, we can say that less than that is approximately 16% of boxes.

Quantity B:
64 pounds is two standard deviation above the mean. Following the image, we can say that more than that is approximately 2% of boxes.


A>B
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Re: Parts at a factory are packed into shipping containers. The weights o [#permalink] New post   31 Aug 2022, 10:24
Solution -

The quantity in Column A is greater.

The values of 43 and 64 fall at one and two standard deviations, respectively, away from the mean. In a normal distribution, approximately 34% of the data falls within one standard deviation above, and another 34% below, the mean. Approximately 14% of the data falls between the first and the second standard deviation on each side of the mean, and approximately 2% of the data is found between the second and third standard deviation marks on each side of the mean. Altogether, across six standard deviations, 2% + 14% + 34% + 34% + 14%+ 2% = 100% of the data. The percentages below 43 (one standard deviation below the mean of 50) are 14% and 2%, or 16%. The percentage above 64 (two standard deviations above the mean) is only 2%. The theoretical normal distribution extends to infinity in both directions, but we must be talking about a reasonably finite number of packages.
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