PSAT Question

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vmaskey

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Development of a Bee
Stage Duration
Egg 2 days
Larva 1 week
Pupa 5 days
Adult 2 weeks

A honeybee must develop through 4 stages to become a full-grow adult. The lenth and stages of the bee's development are show in the table above. In a controlled environment, a queen bee produces new eggs at a costant rate throughout a four-week period. If 200 of these developing bees were randomly selected at the end of this period, how many larvae would we expect to find?
 
vmaskey said:
Development of a Bee
Stage Duration
Egg 2 days
Larva 1 week
Pupa 5 days
Adult 2 weeks

A honeybee must develop through 4 stages to become a full-grow adult. The lenth and stages of the bee's development are show in the table above. In a controlled environment, a queen bee produces new eggs at a costant rate throughout a four-week period. If 200 of these developing bees were randomly selected at the end of this period, how many larvae would we expect to find?
Click to expand...
Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:


Please share your work/thoughts about this problem.
 
vmaskey said:
Development of a Bee
Stage Duration
Egg 2 days
Larva 1 week
Pupa 5 days
Adult 2 weeks

A honeybee must develop through 4 stages to become a full-grow adult. The lenth and stages of the bee's development are show in the table above. In a controlled environment, a queen bee produces new eggs at a costant rate throughout a four-week period. If 200 of these developing bees were randomly selected at the end of this period, how many larvae would we expect to find?
Click to expand...
Do you see that the four stages add up to 4 weeks? Do you see how that's relevant?

During what fraction of its life is a given individual a larva?
 
Dear Mr. Subhotosh Khan,

I myself need help solving the problem. I don't know how to proceed. My guess is 50 but not sure why right answer is 100.
 
vmaskey said:
Dear Mr. Subhotosh Khan,

I myself need help solving the problem. I don't know how to proceed. My guess is 50 but not sure why right answer is 100.
Click to expand...
Can you answer the questions posed in response #3 above?
 
vmaskey said:
I don't know how to proceed. My guess is 50 but not sure why right answer is 100.
Click to expand...
I would have said 50, too.

Are you saying that someone told you it is 100? Please tell us more about it -- was this answer given in a book, or by software, or by your teacher, or by a friend, or what? Also, if you didn't quote the entire problem word for word, please do so, in case there is some detail that changes the answer.

Then we can try to figure out where a mistake was made. Books and people (and even software) can be wrong. So can you and I.
 
Dear Dr. Peterson,

The answer is in the book. But it has not shown how it has been calculated. It simply says answer is 100. So I need to know if answer is correct.
 
At the end of 4 weeks chances of selecting each of them is 1/4. So out of 200 of them chances of selecting larvae is 50. Otherwise chances of selecting each of them should be 1/2 out of 200 for the answer to be 100. So I don't know if chances of selecting each of them should be 1/4 or 1/2.
 
The answer is 50 but we are concerned that you say that you guessed 50 was the answer. Can you show us your work so we can if you did the problem correctly?
 
1/4 ( 200) = 50

This is my answer. Please do correct me if I'm wrong.

Jomo said:
The answer is 50 but we are concerned that you say that you guessed 50 was the answer. Can you show us your work so we can if you did the problem correctly?
Click to expand...
 
vmaskey said:
1/4 ( 200) = 50................This is my answer. Please do correct me if I'm wrong.
Click to expand...
Why did you use (1/4)?

Why did you use (200)?

What equation did you use to multiply that (1/4) by that 200?
 
Chances of random selection of either egg, pupa, larvae or adult at the end of 4 weeks is 1/4.That is 1/4 chances of selecting larvae among 4 catagories. And we are selecting 200 of them ( egg, larvae, pupa and adult ) randomly. It means chances of selecting larvae among 200 of them is : 1/4 ( 200 ) = 50
 
vmaskey said:
Chances of random selection of either egg, pupa, larvae or adult at the end of 4 weeks is 1/4.That is 1/4 chances of selecting larvae among 4 catagories. And we are selecting 200 of them ( egg, larvae, pupa and adult ) randomly. It means chances of selecting larvae among 200 of them is : 1/4 ( 200 ) = 50
Click to expand...

Thank you. But is my logic really right ?
 
vmaskey said:
Chances of random selection of either egg, pupa, larvae or adult at the end of 4 weeks is 1/4.That is 1/4 chances of selecting larvae among 4 catagories. And we are selecting 200 of them ( egg, larvae, pupa and adult ) randomly. It means chances of selecting larvae among 200 of them is : 1/4 ( 200 ) = 50
Click to expand...
Your logic is correct - but the last sentence needs editing.
You said:

It means chances of selecting larvae among 200 of them is : 1/4 ( 200 ) = 50​
​
I would say:

It means chances of selecting expected value of number of larvae among 200 of them is : 1/4 ( 200 ) = 50​

I would NOT use words like "chance" or "probability" associated with outcome > 1
 
Dear friends,

I found the right answer of the above mentioned math problem with the explanation. The answer is 100 NOT 50. And explanation is :

Bees are in the larval stage for 1 out of the 2 weeks of their development (we don’t count the two weeks of adulthood as “developing”), so selecting 200 at random should give ½ × 200 = 100 bees in the larval stage.
 
vmaskey said:
Dear friends,

I found the right answer of the above mentioned math problem with the explanation. The answer is 100 NOT 50. And explanation is :

Bees are in the larval stage for 1 out of the 2 weeks of their development (we don’t count the two weeks of adulthood as “developing”), so selecting 200 at random should give ½ × 200 = 100 bees in the larval stage.
Click to expand...
Okay, I missed that!!
 
vmaskey said:
Dear friends,

I found the right answer of the above mentioned math problem with the explanation. The answer is 100 NOT 50. And explanation is :

Bees are in the larval stage for 1 out of the 2 weeks of their development (we don’t count the two weeks of adulthood as “developing”), so selecting 200 at random should give ½ × 200 = 100 bees in the larval stage.
Click to expand...
I think it's a very poorly written trick question. Look at the wording:

vmaskey said:
Development of a Bee
Stage Duration
Egg 2 days
Larva 1 week
Pupa 5 days
Adult 2 weeks

A honeybee must develop through 4 stages to become a full-grow adult. The length and stages of the bee's development are show in the table above. In a controlled environment, a queen bee produces new eggs at a constant rate throughout a four-week period. If 200 of these developing bees were randomly selected at the end of this period, how many larvae would we expect to find?
Click to expand...
It describes all four stages as "stages of development". Then we select "200 of these developing bees". It doesn't say that the adults have left and only those still in the first stages are available to select from, though you can argue for that view; it says "these", which implies "all these". I think it is intentionally misleading, at best, and the author deserves to be thrown into the hive without a bee suit.

I presume this isn't a real PSAT problem, but somebody's idea of one for practice. I've seen a lot of so-called practice problems for such exams that are nothing like the real thing. Where did you get this? And where did you get the "right answer"?
 
Dr.Peterson said:
I think it's a very poorly written trick question. Look at the wording:


It describes all four stages as "stages of development". Then we select "200 of these developing bees". It doesn't say that the adults have left and only those still in the first stages are available to select from, though you can argue for that view; it says "these", which implies "all these". I think it is intentionally misleading, at best, and the author deserves to be thrown into the hive without a bee suit.

I presume this isn't a real PSAT problem, but somebody's idea of one for practice. I've seen a lot of so-called practice problems for such exams that are nothing like the real thing. Where did you get this? And where did you get the "right answer"?
Click to expand...

Ivy Global New PSAT
 
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