STATISTICS HAALP

[origamimommy]

Help me!!  I can't think right now, and we just got a "pop" quiz that is due by six.  Omfg, can someone please help me?

1. The height of maple trees in Ohio is approximately Normally distributed, with an average of 74 feet and a standard deviation of 8 feet.





a) What proportion of maple trees are between 66 and 82 feet?





b) What proportion of maple trees are between 58 and 74 feet?





c) What proportion of maple trees are between 90 and 98 feet?





d) What proportion of maple trees are taller than 74 feet?





e) What proportion of maple trees are taller than 82 feet?





f) What proportion of maple trees are shorter than 90 feet?



2. The speed limit on a particular freeway is 65 mph. A radar system revealed that the actual speed of traffic is approximately Normally distributed, with an average of 68 mph and a standard deviation of 4 mph.



a) What proportion of cars exceed the speed limit?





b) What proportion of cars go faster than 75 mph?





c) What proportion of cars go between 65 and 75 mph?





d) How slow are the slowest 5% of drivers going?

[paddyb]

. The height of maple trees in Ohio is approximately Normally distributed, with an average of 74 feet and a standard deviation of 8 feet.





a) What proportion of maple trees are between 66 and 82 feet?
68.2%




b) What proportion of maple trees are between 58 and 74 feet?

47.7%



c) What proportion of maple trees are between 90 and 98 feet?

2.2



d) What proportion of maple trees are taller than 74 feet?

50%



e) What proportion of maple trees are taller than 82 feet?


15.9%


f) What proportion of maple trees are shorter than 90 feet?
97.7%


2. The speed limit on a particular freeway is 65 mph. A radar system revealed that the actual speed of traffic is approximately Normally distributed, with an average of 68 mph and a standard deviation of 4 mph.



a) What proportion of cars exceed the speed limit?





b) What proportion of cars go faster than 75 mph?





c) What proportion of cars go between 65 and 75 mph?





d) How slow are the slowest 5% of drivers going?

[paddyb]

so those are the first ones. In percentages (is that what you wanted?)

[paddyb]

p.s. i based my answers off of this en.wikipedia.org/wiki/Standard_deviation

[paddyb]

also,

en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule

[paddyb]

let me know if you want me to explain something. Granted I am just guessing/assuming that the distribution on wiki is right.

[origamimommy]

Oh my gosh, you are a lifesaver! Thank you. I am working on the second problem right now. THANK YOU!!

[paddyb]

double check my math on the first.

[origamimommy]

Okay, thanks!

[origamimommy]

I am still confused. Can you give me the formula you used?

[paddyb]

So I didn't use a formula. I used the standard curve from the wiki (which shows the percentages) and above each line wrote down a number so above the mid line -74, above the one to the right of middle 82, the one left of middle 66 etc. Then added the percentages necessary depending on the question.
50% is to the left of 74 and 50% to the right.

Also sum total of one standard deviation from the mean (in both directions) is 68 or 68.2 (depending on how specific you are getting)

[origamimommy]

Feb 5, 2015 17:13:28 GMT -5 paddyb said:

So I didn't use a formula. I used the standard curve from the wiki (which shows the percentages) and above each line wrote down a number so above the mid line -74, above the one to the right of middle 82, the one left of middle 66 etc. Then added the percentages necessary depending on the question.
50% is to the left of 74 and 50% to the right.

Also sum total of one standard deviation from the mean (in both directions) is 68 or 68.2 (depending on how specific you are getting)

I honestly just can't understand this.  I don't  know what is going on.  I have been fine all semester and now I feel like I am just going to bomb the final.  I can't figure out how to calculate this out with the information I am finding.  I feel like a complete moron.

[origamimommy]

Just clicked. Gah, I feel so stupid.

[paddyb]

[paddyb]

wow that was big.

so for a normal distribution the mean (74 ft) is right in the middle of the bell curve. the mean by definition had 50% above and 50% below.

we know the deviation is 8 feet so -1(symbol) and 1 (symbol) are 66 and 82 from the first question. looking at the curve that is 68.2% (34.1 plus 34.1). also, that is just a fact to memorize (approx. 68% are within on deviation to the right and left)

[paddyb]

glad to hear it clicked!