Assuming that the population is normally distributed, construct a $95\%$ confidence interval for the population mean for each of the samples below. Explain why these two samples produce different confidence intervals even though they have the same mean and range.

Sample A: $1,4,4,4,5,5,5,8$

Full data set

Construct a $95\%$ confidence interval for the population mean for sample A$.$

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$($Type integers or decimals rounded to two decimal places as needed.$)$