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27 May 2022, 01:30
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Difficulty:
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76% (01:57) correct
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46, 54, 58, 67, 77, 79, 97, 98, 99
The list above shows the scores of nine students obtained on a scheduled test. If the standard deviation of the nine scores is 19.51, how many of the scores are greater than one standard deviation above the mean of the nine scores?
(A) One
(B) Two
(C) Three
(D) Four
(E) Five
Are You Up For the Challenge: 700 Level Questions
The list above shows the scores of nine students obtained on a scheduled test. If the standard deviation of the nine scores is 19.51, how many of the scores are greater than one standard deviation above the mean of the nine scores?
(A) One
(B) Two
(C) Three
(D) Four
(E) Five
Are You Up For the Challenge: 700 Level Questions
27 May 2022, 01:59
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Given : The scores of 9 students on a scheduled test - 46, 54, 58, 67, 77, 79, 97, 98, 99
Standard deviation (σ) = 19.51
To find : How many of the scores are greater than Mean + 1σ
Solution : The problem is approached as follows :
a) Find the mean of the 9 numbers
b) Compute the value of Mean + σ = Mean + 19.51
c) Count the scores greater than this value
On computation, Mean = (46 + 54 + 58 + 67 + 77 + 79 + 97 + 98 + 99)/9 = 75
Therefore, Mean + σ = 75 + 19.51 = 94.51
From this, we see that only 3 scores (97,98 and 99) are greater than 94.51.
C) is the right answer
Standard deviation (σ) = 19.51
To find : How many of the scores are greater than Mean + 1σ
Solution : The problem is approached as follows :
a) Find the mean of the 9 numbers
b) Compute the value of Mean + σ = Mean + 19.51
c) Count the scores greater than this value
On computation, Mean = (46 + 54 + 58 + 67 + 77 + 79 + 97 + 98 + 99)/9 = 75
Therefore, Mean + σ = 75 + 19.51 = 94.51
From this, we see that only 3 scores (97,98 and 99) are greater than 94.51.
C) is the right answer
Mean: \(\frac{46 + 54 + 58 + 67+ 77 + 79 + 97 + 98 + 99 }{ 9} = 75\)
One std. greater than the mean: \(75+19.51 = 94.51\)
All numbers greater than 94.51: \(97, 98\) & \(99\)
Answer C
One std. greater than the mean: \(75+19.51 = 94.51\)
All numbers greater than 94.51: \(97, 98\) & \(99\)
Answer C
