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#1
03-09-2013
 USMLE Forums Scout Steps History: Not yet Posts: 96 Threads: 10 Thanked 24 Times in 23 Posts Reputation: 34
Normal Distribution Values Calculation

In a random survey of 3,015 boys age 11, the average height was 146 cm, and the standard deviation (SD) was 8 cm. A histogram suggested the heights were approximately normally distributed. Fill in the blanks.
a.*One boy was 170 cm tall. He was above average by__ SDs.
b. Another boy was 148 cm tall. He was above average by __ SDs.
c.*A third boy was 1.5 SDs below the average height. He was __cm tall.
d.*If a boy was within 2.25 SDs of average height, the shortest he could have been is __ cm and the tallest is __ cm.
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If you do not hope, you will not find what is beyond your hopes.

#2
03-10-2013
 USMLE Forums Scout Steps History: Step 1 Only Posts: 21 Threads: 0 Thanked 11 Times in 10 Posts Reputation: 21

I think you can use the "three rule" and find out the SDs and heights

Average is 146cm with SD of 8.

a. This kid is 170cm , which is 24cm above the mean. If 8cm is 1 SD, then 24cm must be 3SDs above average.

b. This kid is 148, which is just 2 cm above the mean. If 8 cm is 1 SD, then 2 cm must be 0.25 SD above the mean

C. This kid is 1.5 SD below the height, which corresponds to 12 cm below average, so he must be 134 cm.

d. 2.25 SD is 18 cm. (If 1 SD is 8, then 2.25 is 18 cm) So he must be at least 128 cm and at most 164.

I am not 100% sure if this is how you answer this, but if someone knows any other way please let me know.

Best
#3
03-10-2013
 USMLE Forums Veteran Steps History: CS Only Posts: 219 Threads: 44 Thanked 44 Times in 33 Posts Reputation: 54

I came up with the same answers
#4
03-10-2013
 USMLE Forums Scout Steps History: Not yet Posts: 96 Threads: 10 Thanked 24 Times in 23 Posts Reputation: 34

Quote:
 Originally Posted by rafdelag I think you can use the "three rule" and find out the SDs and heights Average is 146cm with SD of 8. a. This kid is 170cm , which is 24cm above the mean. If 8cm is 1 SD, then 24cm must be 3SDs above average. b. This kid is 148, which is just 2 cm above the mean. If 8 cm is 1 SD, then 2 cm must be 0.25 SD above the mean C. This kid is 1.5 SD below the height, which corresponds to 12 cm below average, so he must be 134 cm. d. 2.25 SD is 18 cm. (If 1 SD is 8, then 2.25 is 18 cm) So he must be at least 128 cm and at most 164. I am not 100% sure if this is how you answer this, but if someone knows any other way please let me know. Best
Man your answer was great, and u solved it so smoothly. But i found the answer to this with these freaky formulas. do u know about these formulas, could u plz explain them also ?
(a) z= (x-m)/s = (170-146)/8 = 3
(b) z = (148 - 146)/8 = 0.25
(c) x = m + z * s = 146 + (-1.5)(8) = 134
(d) x = m + z * s
x1 = 146 + (-2.25)(8) = 128 and x2 = 146 + 2.25 * 8 = 164.
__________________
If you do not hope, you will not find what is beyond your hopes.
#5
03-10-2013
 USMLE Forums Scout Steps History: Step 1 Only Posts: 21 Threads: 0 Thanked 11 Times in 10 Posts Reputation: 21

Quote:
 Originally Posted by dr.ali2011 Man your answer was great, and u solved it so smoothly. But i found the answer to this with these freaky formulas. do u know about these formulas,could u plz explain them also ? (a) z= (x-m)/s = (170-146)/8 = 3 (b) z = (148 - 146)/8 = 0.25 (c) x = m + z * s = 146 + (-1.5)(8) = 134 (d) x = m + z * s x1 = 146 + (-2.25)(8) = 128 and x2 = 146 + 2.25 * 8 = 164.
It basically the same concept.

Z= z score

A z score indicates how far the observed data is above or below the mean.

1 SD = Z score of 1.

If you look at the formula for a) it says z score = x-m/s
x = the height you got (170)
m = mean (146)
s= standard deviation, which in this case is 8
so your z score in this case is 3, which is 3 SD
#6
03-11-2013
 USMLE Forums Scout Steps History: Not yet Posts: 96 Threads: 10 Thanked 24 Times in 23 Posts Reputation: 34

Quote:
 Originally Posted by rafdelag It basically the same concept. Z= z score A z score indicates how far the observed data is above or below the mean. 1 SD = Z score of 1. If you look at the formula for a) it says z score = x-m/s x = the height you got (170) m = mean (146) s= standard deviation, which in this case is 8 so your z score in this case is 3, which is 3 SD
Thanx bro, may i ask which source u use for statistics ? This subject always gets me
__________________
If you do not hope, you will not find what is beyond your hopes.
#7
03-11-2013
 USMLE Forums Scout Steps History: Step 1 Only Posts: 21 Threads: 0 Thanked 11 Times in 10 Posts Reputation: 21

Quote:
 Originally Posted by dr.ali2011 Thanx bro, may i ask which source u use for statistics ? This subject always gets me
I studied from Kaplan notes and Kaplan lecture videos. Videos are in my opinion better to understand statistics because they give good example problems and solve them with you.

Best

 Tags Biostatistics-Epidemiology, Step-1-Questions

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