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#1




Normal Distribution Values Calculation
Plz give your answer with the explanation
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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#2




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




I came up with the same answers



#4




Quote:
(a) z= (xm)/s = (170146)/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.
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If you do not hope, you will not find what is beyond your hopes. 
#5




Quote:
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 = xm/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




Quote:
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If you do not hope, you will not find what is beyond your hopes. 
#7




Quote:
Best 
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BiostatisticsEpidemiology, Step1Questions 
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