SOLUTION: In 2012, 1,664,479 students took the SAT exam. The distribution of scores in the verbal section of the SAT had a mean µ = 496 and a standard deviation σ = 114. Let X = a SAT exam

Algebra ->  Probability-and-statistics -> SOLUTION: In 2012, 1,664,479 students took the SAT exam. The distribution of scores in the verbal section of the SAT had a mean µ = 496 and a standard deviation σ = 114. Let X = a SAT exam      Log On


   

Question 1173830: In 2012, 1,664,479 students took the SAT exam. The distribution of scores in the verbal section of the SAT had a mean µ = 496 and a standard deviation σ = 114. Let X = a SAT exam verbal section score in 2012. Then X ~ N(496, 114). -Billy scored 334. Find the z-scores for 334 to the nearest tenth. z=_________ -Xito scored 375. Find the z-scores for 375 to the nearest tenth. z=________ -Which student scored better based on their z score, Billy or Xito?
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
 

Hi,



Normal Distribution:

µ = 496  ,   σ = 114      z+=+blue%28x+-+mu%29%2Fblue%28sigma%29

X%5BBilly%5D+=+334+

 z = (334-496)/114  = -1.4 (nearest tenth)

X%5BXito%5D+=+375+

 z = (375 - 496)/114 = -1.1

Which student scored better based on their z score, Billy or Xito

  -1.4 < -1.1   Billy z-score further away from the mean.

Wish You the Best in your Studies.



For the normal distribution: 

one  standard deviation from the mean accounts for about 68.2% of the set 

two standard deviations from the mean account for about 95.4%

and three standard deviations from the mean account for about 99.7%.

Important to Understand z -values as they relate to the Standard Normal curve: