The mean and the standard deviation of the 8 numbers shown

Question

9.4 , 9.9 , 9.9 , 9.9 , 10.0 , 10.2 , 10.2 , 10.5 
The mean and the standard deviation of the 8 numbers shown above is 10 and 0.3 respectively. What percent of the 8 numbers are within 1 standard deviation of the mean?

A. 90% 
B. 85% 
C. 80% 
D. 75% 
E. 70%

Bunuel · Accepted Answer

9.4 , 9.9 , 9.9 , 9.9 , 10.0 , 10.2 , 10.2 , 10.5
The mean and the standard deviation of the 8 numbers shown above is 10 and 0.3 respectively. What percent of the 8 numbers are within 1 standard deviation of the mean?

A. 90%
B. 85%
C. 80%
D. 75%
E. 70%

"Within 1 standard deviation of the mean" - means in the range {mean-1*sd; mean+1*sd} = {10-*0.3; 10+0.3} = {9.7; 10.3}.

From the 8 listed numbers, 6 are within this range so 6/8=75%.

Answer: D.

Bunuel · Answer

rhine29388 · Answer

The phrase ' Within one standard deviation ' actually means the values which lie in the (10 - 0.3) and (10 + 0.3)
So we have see which values lie between 9.7 and 10.3
clearly 6 values from the given list lie within one standard deviation
percent of values which lie within one SD =  \frac{6}{8}  * 100 = 75%
correct answer - D

LogicGuru1 · Answer

Mean = 10; SD=0.3
Range of values below 1 SD = Mean - 1 SD 
Range = 10-0.3 to 10+0.3 = 10.30 to 9.70

9.4 , 9.9 , 9.9 , 9.9 , 10.0 , 10.2 , 10.2 , 10.5

Outside the range = 9.4 and 10.5 ; total 2/8 
 Inside the range 9.9 , 9.9 , 9.9 , 10.0 , 10.2 , 10.2 ; total 6/8

6/8 = 0.75 or 75%
ANSWER IS D

MathRevolution · Answer

Mean: 10
Standard Deviation: 0.3

Within '1' standard deviation from mean: 10 +0.3 = 10.3 and 10-0.3 = 9.7

=> Numbers from 9.7 to 10.3: 9.9, 9.9, 9.9, 10.0, 10.2, 10.2

=> Percent of numbers: 6 out of 8 = 75%

Answer D

MHIKER · Answer

Within 1 standard deviation means the are which are greater than (10.0-0.3) 9.7 and less than 10.30, There are 6 such numbers.

So,  \frac{6}{8}*100=75 %

The answer is  D

praveen27sinha · Answer

9.4 , 9.9 , 9.9 , 9.9 , 10.0 , 10.2 , 10.2 , 10.5
The mean and the standard deviation of the 8 numbers shown above is 10 and 0.3 respectively. What percent of the 8 numbers are within 1 standard deviation of the mean?

A. 90%
B. 85%
C. 80%
D. 75%
E. 70%

Range of 1 Sd = 10-.3 to 10+.3
 = 9.7 to 10.3
Numbers in range :- 9.4,10,10.2
total number are 6
%=(6/8)*100 = 75%
Ans D

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The mean and the standard deviation of the 8 numbers shown

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The mean and the standard deviation of the 8 numbers shown

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