Question

For a given distribution the average is 15.5 and the standard deviation is 1.5. If a sample is taken at random, which value is most likely? 20.2 10.1 16.3 12.9

Answer 1

Given:
average 15.5
standard deviation 1.5

Allowable range: 15.5 + 1.5 = 17 ; 15.5 - 1.5 = 14

The sample must be between 14 and 17 to still be within the standard deviation. Among the choices, only 16.3 is within the limit.

16.3 is the value most likely to be taken as a sample.

Answer 2

The standard deviation is  the square root of the variance.The variance is  the average squared deviation of each number from its mean.

The given  average 15.5   standard deviation 1.5.

The  range will be in between the sum and difference of the average and standard deviation.= 15.5+1.5= 17 and 15.5-1.5= 14.

The numbers should be  be between 14 and 17 so as to have standard Deviation of 15. Among the given options 16.3 lie between 14 and 17 and hence the correct answer.