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A normal distribution has = 20 and = 4. What is the probability of randomly sele

ID: 3126564 • Letter: A

Question

A normal distribution has = 20 and = 4. What is the probability of randomly selecting a score greater than 25 from this distribution?

E. None of the above.

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A normal distribution has a mean of µ = 40 with = 8. If one score is randomly selected from this distribution,

what is the probability that the score will be less than X = 34?

D. 0.4532 or 45.32%

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A normal distribution has a mean of µ = 80 with = 20. What score separates the highest 15% of the distribution from the rest of the scores? (Note: use the closest value listed in the Unite Normal table).

A. 0.3944 or 39.44% B. 0.1056 or 10.56% C. 0.8944 or 89.44% D. 0.7888 or 78.88%

E. None of the above.

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A normal distribution has a mean of µ = 40 with = 8. If one score is randomly selected from this distribution,

what is the probability that the score will be less than X = 34?

A. 0.7734 or 77.34% B. 02266 or 22.66% C. 0.2734 or 27.34%

D. 0.4532 or 45.32%

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A normal distribution has a mean of µ = 80 with = 20. What score separates the highest 15% of the distribution from the rest of the scores? (Note: use the closest value listed in the Unite Normal table).

A. X = 59.2 B. X = 100.8 C. X = 95 D. X = 65

Explanation / Answer

1.

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    25      
u = mean =    20      
          
s = standard deviation =    4      
          
Thus,          
          
z = (x - u) / s =    1.25      
          
Thus, using a table/technology, the right tailed area of this is          
          
P(z >   1.25   ) =    0.105649774 [ANSWER, B]

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2.

We first get the z score for the critical value. As z = (x - u) / s, then as          
          
x = critical value =    34      
u = mean =    40      
          
s = standard deviation =    8      
          
Thus,          
          
z = (x - u) / s =    -0.75      
          
Thus, using a table/technology, the left tailed area of this is          
          
P(z <   -0.75   ) =    0.226627352 [ANSWER, B]

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3.

First, we get the z score from the given left tailed area. As          
          
Left tailed area =    0.85      
          
Then, using table or technology,          
          
z =    1.036433389      
          
As x = u + z * s,          
          
where          
          
u = mean =    80      
z = the critical z score =    1.036433389      
s = standard deviation =    20      
          
Then          
          
x = critical value =    100.728667-->100.8 [closest, OPTION B]

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