In a study on infants, one of the characteristics measured was head circumference. The mean head circumference of $14$ infants was $34\mathrm{.}1$ centimeters $($cm$).$ Complete parts $($a$)$ through $($d$)$ below.

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a$.$ Assuming that head circumferences for infants are normally distributed with standard deviation $2\mathrm{.}2cm,$ determine a $90\%$ confidence interval for the mean head circumference of all infants.

The confidence interval for the mean head circumference of all infants is from $,cm$ to $,cm.($Round to one decimal place as needed.$)$

b$.$ Obtain the margin of error, $E,$ for the confidence interval you found in part $($a$).$

The margin of error is $cm.$

$($Round to one decimal place as needed.$)$

c$.$ Explain the meaning of $E$ in this context in terms of the accuracy of the estimate. Choose the correct answer below and fill in the answer box to complete your choice.

$($Round to one decimal place as needed.$)$

A$.$ We can be $90\%$ confident that the estimate of $$ by $\stackrel{}{x}$ is $cm.$

B$.$ We can be $90\%$ confident that the error made in estimating $$ by $\stackrel{}{x}$ is at most $cm.$

C$.$ We can be $90\%$ confident that the error made in estimating $$ by $\stackrel{}{x}$ is at least $,cm.$

D$.$ We can be $90\%$ confident that the possible values of $$ are within $,cm$ of each other.