Evaluate $E=z^{} \sqrt{\frac{\sigma_{1}^{2}}{n_{1}}+\frac{\sigma_{2}^{2}}{n_{2}}}$ for $z^{}=1.39, \sigma_{1}=0.75, \sigma_{2}=0.71, n_{1}=15$, and $n_{2}=42$.
$E=\square$ (Round to two decimal places as needed.)

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Answer

Rounding to two decimal places, we get the final answer as $E=\boxed{0.31}$

Steps

Step 1 ：Given values are $z^{*}=1.39, \sigma_{1}=0.75, \sigma_{2}=0.71, n_{1}=15$, and $n_{2}=42$

Step 2 ：Substitute the given values into the expression $E=z^{*} \sqrt{\frac{\sigma_{1}^{2}}{n_{1}}+\frac{\sigma_{2}^{2}}{n_{2}}}$

Step 3 ：After calculation, we get $E=0.30926291442411136$

Step 4 ：Rounding to two decimal places, we get the final answer as $E=\boxed{0.31}$