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Sagot :
The standard deviation can be calculated using the formula:
[tex]\sigma=\sqrt[]{\frac{\sum ^{}_{}(x_i-\mu)^2}{N-1}}[/tex]Where N is the number of observations, x_i is each observation and μ is the mean. From that, we can see that, for the standard deviation be zero,
[tex](x_i-\mu)^2=0[/tex]For all observations. This meas that all of the 100 observations must be the same value and equal to the mean:
[tex]\begin{gathered} (x_i-\mu)^2=0 \\ x_i-\mu=0 \\ x_i=\mu=40 \end{gathered}[/tex]If all observations are equal to 40, so is the smallest observations. So, the smallest observation must be equal to 40, which is alternative D.
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