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Suppose that the IQ scores of students at a certain college follow a normal distribution with mean 115 and standard deviation 12.

a. Use the normal model to determine the proportion of students with an IQ score below 100.

b. Find the proportion of these undergraduates having IQs greater than 130.

c.Find the proportion of these undergraduates having IQs between 110 and 130.

d.With his IQ of 75, what would the percentile of Forrest Gump’s IQ be?

e.Determine how high one’s IQ must be in order to be in the top 1% of all IQs at this college.

 

I'm really sick, I have about 13 pages of this type of homework, and I've been stuck on this for hours now. Please help me with this and show how I can solve these because I need to understand. Thank you in advance.

 Feb 12, 2020
 #1
avatar+22108 
+2

A.   Mean is 115      s.d. = 12       100 score will be   15 points below the mean , or   15/12 = 1.25 standard deviations below the mean

 

Look at you table of negative  z-scores and find the number corresponding to   -1.25    z = .1056

   .1056 x 100 % = 10.56%     with score below 100

 

 

B.  Greater than 130    is    15 points above the mean    15/12 = 1.25 ABOVE the mean

     look at your positive  z-score table  for z-score =1.25       .8944   of the students had a score LESS than this

               so    1 - .8944  = .1056      or 10.56%   were higher than 130

 

C   calculate the z score less than 110       calculate the z score less than 130

                               z130 - z110   =   fraction between 130 and 100

 

D.   FInd z   for 75   (  115 - 75  = 40 BELOW        40/12 =  - 3.33  z  )     from neg z-score table  

E.   Find positive z-score = .9900       (9901 is the closest in my table)      this equals z -score   2.33

            2.33  x 12 s.d.    = 27.96     then       115 + 27.96 = 142.96 to be 1%

 Feb 12, 2020
 #2
avatar+109740 
0

Good work, EP    !!!!

 

cool cool cool

CPhill  Feb 12, 2020
 #3
avatar+22108 
+1

Thanx, MathGuru !  cheeky            ......gotta go shovel snow...wooohooo!

ElectricPavlov  Feb 12, 2020

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