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1. Find z (a standardized score), given the following. (Give your answer correct

ID: 3131691 • Letter: 1

Question

1. Find z (a standardized score), given the following. (Give your answer correct to two decimal places.)

x = 246, = 215 and = 11.6

z =  

2. Final averages are typically approximately normally distributed with a mean of 72 and a standard deviation of 10. Your professor says that the top 8% of the class will receive an A; the next 24%, a B; the next 36%, a C; the next 20%, a D; and the bottom 12%, an F. (Give your answers correct to one decimal place.)

(a) What average must you exceed to obtain an A?


(b) What average must you obtain to pass the course? (You'll need a D or better.)

Explanation / Answer

1.

As

z = (x-u)/sigma

Then

z = (246-215)/11.6 = 2.672413793 [ANSWER]

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2.

a)

First, we get the z score from the given left tailed area. As          
          
Left tailed area = 1 - 0.08 =   0.92      
          
Then, using table or technology,          
          
z =    1.40507156      
          
As x = u + z * s,          
          
where          
          
u = mean =    72      
z = the critical z score =    1.40507156      
s = standard deviation =    10      
          
Then          
          
x = critical value =    86.05071 = 86.1 [ANSWER]

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B)

You should not be on the bottom 12%, then.

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.12      
          
Then, using table or technology,          
          
z =    -1.174986792      
          
As x = u + z * s,          
          
where          
          
u = mean =    72      
z = the critical z score =    -1.174986792      
s = standard deviation =    10      
          
Then          
          
x = critical value =    60.25013208 = 60.3 [ANSWER]