Don\'t need (a) If the results on a nationally administered introductory statist

Question

Don't need (a)

If the results on a nationally administered introductory statistics exam is normally distributed with a mean of 100 points and a standard deviation of 8 points, determine the following: (a)

Don't need (a)

(b) Find the z-score for a single exam that had 110 points. Then find the z-score for one with 80 points. (c) If x represents a possible point-score on the exam, find P(x < 110). (d) Find P(80 < x < 110) and give an interpretation of this value. (e) What is the minimum number of points one must score on this exam if they want to be in the top 35% of all the scores?

Explanation / Answer

B)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    110      
u = mean =    100      
          
s = standard deviation =    8      
          
Thus,          
          
z = (x - u) / s =    1.25   [ANSWER]

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c)

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    110      
u = mean =    100      
          
s = standard deviation =    8      
          
Thus,          
          
z = (x - u) / s =    1.25      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   1.25   ) =    0.894350226 [ANSWER]

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d)

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    80      
x2 = upper bound =    110      
u = mean =    100      
          
s = standard deviation =    8      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -2.5      
z2 = upper z score = (x2 - u) / s =    1.25      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.006209665      
P(z < z2) =    0.894350226      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.888140561   [ANSWER]

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e)

First, we get the z score from the given left tailed area. As          
          
Left tailed area = 1 - 0.35 =   0.65      
          
Then, using table or technology,          
          
z =    0.385320466      
          
As x = u + z * s,          
          
where          
          
u = mean =    100      
z = the critical z score =    0.385320466      
s = standard deviation =    8      
          
Then          
          
x = critical value =    103.0825637   [ANSWER]  
  

     

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