Hi, Could you please help me with this question? -The collage boards, whic sre a

Question

Hi,

Could you please help me with this question?

-The collage boards, whic sre administered each year to many thousands of highschool students, are scored so as to yield a mean of 500 and a standart deviation of 100. These scores are close to being normal distributed. An exclusive club wishes to invite in the top 10% on the collage boards to join.

a) What score is required to be invited to join the club?

b) what score seperates the top 60% of the poulation from the bottom 40% ? What do we call this value?

Thanks in advance!

Explanation / Answer

a)

First, we get the z score from the given left tailed area. As          
          
Left tailed area = 1 - 0.10 =   0.9      
          
Then, using table or technology,          
          
z =    1.281551566      
          
As x = u + z * s,          
          
where          
          
u = mean =    500      
z = the critical z score =    1.281551566      
s = standard deviation =    100      
          
Then          
          
x = critical value =    628.1551566   [ANSWER]

***************************************

b)

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.4      
          
Then, using table or technology,          
          
z =    -0.253347103      
          
As x = u + z * s,          
          
where          
          
u = mean =    500      
z = the critical z score =    -0.253347103      
s = standard deviation =    100      
          
Then          
          
x = critical value =    474.6652897   [ANSWER]  
  
[We call this the 40th percentile.]

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