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STALIN [3.7K]
3 years ago
13

On a 10-item test, three students in Professor Hsin's advanced chemistry seminar received scores of 2, 5, and 8, respectively. F

or this distribution of test scores, the standard deviation is equal to the square root of A) 4. B) 5. C) 6. D) 9
Mathematics
2 answers:
Inessa [10]3 years ago
4 0

Answer:

For this distribution of test scores, the standard deviation is equal to the square root of 9

D) 9

Step-by-step explanation:

We need to know the standard deviation formula:

S=\sqrt{\frac{sum(x-Am)^2}{n-1} } (1)

Where:

S: Standard deviation

sum: Summation

x: Sample values

Am: Arithmetic mean

n:   Number of terms, in this case 3

Now, we need to know the arithmetic mean of the sample values: 2, 5 and 8

Am=\frac{2+5+8}{3} = 5

To know the standard deviation we need to have the summation of each term minus the arithmetic mean squared.

(x-Am)^2 of each term:

(2-5)^2=9\\(5-5)^2=0\\(8-5)^2=9

Now, we can find the standard deviation:

S=\sqrt{\frac{9+0+9}{3-1} } \\S=\sqrt{\frac{18}{2} } \\S=\sqrt{9}

The standard deviation is equal to the square root of 9

docker41 [41]3 years ago
3 0

Answer:

D) 9

Step-by-step explanation:

Standard Deviation is Calculated by formula:  

Standard deviation(\sigma) = Standard deviation(\sigma) = \sqrt{\frac{1}{n-1}\sum_{i=1}^{n}{(x_{i}-\bar{x})^{2}} }

where, \bar{x} is mean of the distribution.

First: Calculating Mean of 2, 5 and 8:

\text{Mean}(\bar x)=\frac{2+5+8}{3} = 5

Then Standard deviation is:

Standard deviation(\sigma) = \sqrt{\frac{1}{3-1}\sum_{i=1}^{n}{(x_{i}-5)^{2}} }

⇒ \sigma = \sqrt{\frac{1}{2}[{(2-5)^{2}}+{(5-5)^{2}}+{(8-5)^{2}} } =\sqrt 9

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Use a system of equations to solve this problem.Bronze is a mix, or alloy, of tin and copper. A metal worker needs 100 g of bron
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Answer:

x = 50 grs

y = 50 grs

Step-by-step explanation:

" x "   is quantity of bronze of 5% tin

" y "   is quantity of bronze of 45% tin

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And the The mathematical expression for the % condition is:

0,05*x  + 0.45*y  = 0,25 * ( x + y )

The system is:

x + y = 100

0,05*x + 0,45*y = 0,25* ( x + y )

Solving this system we get values of x and y

y = 100 - x

0,05*x  + 0,45* ( 100 - x ) = 0,25 * ( x + 100 - x )

0,05*x  + 45 - 0,45*x = 0,25*( 100 )

0,05*x  + 45 - 0,45*x  = 25

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A collection of dimes is arranged in a triangular array with 17 coins in the base row, 16 in the next, 15 in the next, and so fo
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Answer:

153 coins will be there.

Step-by-step explanation:

The number of coin in the bottom row / or last row = 17

The number of coins in the second last row = 16

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|

|

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The number of coins in the second row = 2

The number of coins in the first row = 1

So the total number of coins = (Number of coin in the first row) + (Number of coins in the second row) + (Number of coins in the third row) + ....... + (Number of coins in the last row / seventeenth row)

Total number of coins = 1+2+3+....+16+17

Total number of coins = \frac{17\times(17+1)}{2}=\frac{17\times18}{2}=17\times9=153

(NOTE: Sum of first n natural number = \frac{\boldmath n\times(n+1)}{2})

7 0
3 years ago
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