Question 217463: Can you show the work as well as the problem please.
Problem:
There are 55 blades of grass in 1 in.^2 of lawn. There are 230 blades of grass in 4 in.^2 of the same lawn. How many blades of grass are in 3 in.^2 of lawn?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! 55 blades of grass in 1 square inch of lawn and 230 blades of grass in 4 square inches of lawn.
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because of the variability in each square inch of lawn, there is no way to tell exactly how many blades of grass would be in each square inch of lawn.
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4 * 55 would equal 220 blades of grass which is what you would expect if each square inch of lawn had exactly the same number of blades of grass.
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assuming the 1 square inch of lawn was part of the 4 square inches of lawn, and assuming that the 3 square inches of lawn are what is remaining after you take out the first square inch of lawn, then the three remaining square inches of lawn would contain 230 - 55 blades of grass = 175 blades of grass.
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outside of that, the only way to estimate would be take samples of the whole lawn and determine probabilities from that.
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example:
You sample 100 square inches of lawn.
The average of all the samples is 57 blades of grass in each square inch of lawn.
The standard deviation of all the samples is 3 blades of grass.
Assuming a normal distribution, this means that at a 95% confidence level, you would estimate that each sample would be between 51 blades of grass and 63 blades of grass (to the nearest integer). This means that 95% of the samples taken would have a value between these extremes with 5% having a value outside of these extremes.
If you wanted to know the probability that a sample taken was between 55 and 59, you would get a probability of .495 that this would occur. This means that 49% of the samples would return a value between 55 and 59, assuming a normal distribution.
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Can you determine exactly how many blade of grass in each square inch of lawn?
no.
Can you determine a range of how many blades of grass in each square inch of lawn?
yes.
Can you determine the probability that the range will be within specified limits?
yes, assuming the distribution is normal.
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