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## anonymous one year ago The weights of 1,000 men in a certain town follow a normal distribution with a mean of 150 pounds and a standard deviation of 15 pounds. From the data, what is the number of men weighing more than 165 pounds? What is the number of men weighing less than 135 pounds?

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1. amistre64

so we need to determine the percentage associated with a given z score

2. anonymous

alright.

3. amistre64

what do you have to process this with? ti83? or tables?

4. anonymous

all i have is the data i was given, thats it

5. amistre64

you need to have some means to calculate the stats with.

6. amistre64

how can you take a stats course and not have a method to process a solution?

7. anonymous

i got 159 for the first one. not really sure if its correct

8. amistre64

finding a zscore is relatively simple math ... but converting that to a proper percentage takes tables or a stat calculator/program

9. anonymous

yea thats why this problem is stressing me out

10. amistre64

$z=\frac{x-\mu}{\sigma}$ $z=\frac{165-150}{15}=1$

11. amistre64

so we would need to determine the probability of z>1 in this case. how accurate do we need to be? there is a approximation rule

12. amistre64

64/2 = 34 + 50 = 84 100 - 84 = 16, so about 16% of 1000 would be an estimate, but how good of an estimate do they want?

13. anonymous

there is none, simply says "From the data, we can conclude that the number of men weighing more than 165 pounds is about ___________, and the number of men weighing less than 135 pounds is about _____________."

14. anonymous

im guessing to the nearest whole number?

15. amistre64

135 to 150 is 15 as well, so 1 standard deviation below the mean ... a normal distribution is symetric about the mean so both values should be the same

16. amistre64

P(z<1) = P(z>1) = about 16% using the empirical rule

17. anonymous

yea..

18. amistre64

so, what is 16% of 1000?

19. amistre64

or is it 14%? 50 - 34 = 20 - 4 = 16 .. its 16%

20. anonymous

im lost dude haha

21. amistre64

youve got alot of memorization to tackle for this course :) there is a rule that says about 68% of the data falls within +- 1 sd from the mean the mean is 50, and half of 68 is 34 50 - 34 = 16 .... we have 16% that covers our information ... soo, what is 16% of 1000?

22. amistre64

dinners ready ... good luck

23. anonymous

alright thanks anyways

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