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A set of test scores at a large university is normally distributed wit
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03 Jun 2021, 10:11
03 Jun 2021, 10:11
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A set of test scores at a large university is normally distributed with a mean of 74 and a standard deviation of 7. Which of the following is true?
Indicate all that apply.
A. More students scored above 83 than scored below 63.
B. At least 65% of students scored between 67 and 81.
C. More than half the students scored above 75.
Indicate all that apply.
A. More students scored above 83 than scored below 63.
B. At least 65% of students scored between 67 and 81.
C. More than half the students scored above 75.
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Re: A set of test scores at a large university is normally distributed wit
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03 Jun 2021, 12:12
03 Jun 2021, 12:12
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Carcass wrote:
A set of test scores at a large university is normally distributed with a mean of 74 and a standard deviation of 7. Which of the following is true?
Indicate all that apply.
A. More students scored above 83 than scored below 63.
B. At least 65% of students scored between 67 and 81.
C. More than half the students scored above 75.
Indicate all that apply.
A. More students scored above 83 than scored below 63.
B. At least 65% of students scored between 67 and 81.
C. More than half the students scored above 75.
In Normal Distribution or Bell-curve;
Distribution \(= x̅ ± xσ\)
Where,
\(x̅\) = Mean
\(σ\) = Standard Deviation (SD)
\(x\) = Deviation from the Mean (0 to 3)
1 SD above Mean = \(74 + 7 = 81\)
2 SD above Mean = \(74 + (2)7 = 88\)
3 SD above Mean = \(74 + (3)7 = 95\)
1 SD below Mean = \(74 - 7 = 67\)
2 SD below Mean = \(74 - (2)7 = 60\)
3 SD below Mean = \(74 - (3)7 = 53\)
A. More students scored above 83 than scored below 63
Refer to the graph below; 83 lies between 2 SD and 3 SD above Mean (NEAR to 1 SD) whereas, 63 lies somewhere in the middle of 2SD and 3 SD below Mean. Notice the un-shaded region in the right is greater than the un-shaded region in the left
B. At least 65% of students scored between 67 and 81
Refer to the figure below, approximately \(\frac{2}{3}^{rd}\) of the data lies between 1 SD above and 1 SD below Mean
C. More than half the students scored above 75
In Normal Distribution 50% of data lies above the Mean and 50% data lies below it
Hence, Option A and B
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B. At least 65% of students scored between 67 and 81.png [ 94.41 KiB | Viewed 3958 times ]
A. More students scored above 83 than scored below 63.png [ 15.09 KiB | Viewed 3331 times ]
General Discussion
Re: A set of test scores at a large university is normally distributed wit
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03 Jun 2021, 12:44
03 Jun 2021, 12:44
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stunning explanation KarunMendiratta
