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A fitness trainer wants to estimate the mean grams of protein per serving in weight gainer supplements. He randomly selects twenty different weight gainer supplements and records the grams of protein per serving.

A histogram of these $20$ values shows an approximately normal distribution with a mean and standard deviation of $43.2$ and $5.67\text{ grams}$, respectively.

Which of the following represents a $98$% confidence interval of the average number of grams of protein per serving in weight gainer supplements?

A

$43.2\pm 2.326 \cdot \cfrac { 5.67 }{ \sqrt { 20} }$

B

$43.2\pm 2.528\cdot \cfrac { 5.67 }{ \sqrt { 20} }$

C

$43.2\pm 2.539\cdot \cfrac { 5.67 }{ \sqrt { 20} }$

D

$43.2\pm 2.326\cdot 5.67$

E

$43.2\pm 2.539\cdot 5.67$

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