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Average Number of Text Messages

APSTAT-GEWZVW

A husband was curious at the end of the year about the average number of texts his wife sent out each day. He randomly selected $27$ days and found that the data followed an approximately normal distribution, with a mean of $40.3$ and a standard deviation of $5.4$.

Which of the following represents a $99\%$ confidence interval for the average number of texts his wife sent out each day?

A

$40.3\pm 2.779\cfrac { 5.4 }{ \sqrt { 27 } }$

B

$40.3\pm 2.771\cfrac { 5.4 }{ \sqrt { 27 } }$

C

$40.3\pm 2.576\cfrac { 5.4 }{ \sqrt { 27 } }$

D

$40.3\pm 2.779\cfrac { 5.4 }{ \sqrt { 26 } }$

E

$40.3\pm 2.771\cfrac { 5.4 }{ \sqrt { 26 } }$