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i. The average number of letters sent by $20$participants over the course of a camp session is $7.9$, $\stackrel{¯}{x}=7.9$

ii. The population standard deviation of the number of letters sent by campers throughout a camp session is, $\mathrm{σ}=2.5$

iii. Size of the campers,

$n=20$

During the camp term, a single camper will send home $X$letters, and the average number of letters sent home by $20$campers will be $\stackrel{¯}{X}$.

The problem is solved using the normal distribution. As we all know, the sample size for the population's standard deviation is greater than $30$, and the distribution is $N\left(7.9\begin{array}{c}2.9\\ \sqrt{20}\end{array}\right)$.

i. The confidence interval should be stated.

The confidence interval's output,

$n=20$

$CI=(6.9805,8.8195)$

ii. The graph is as follows:

$6.9805$ $8.8195$

iii. The formula is used to compute the error bound

$EBM=\frac{U_{\text{pper limit-lower limit}}}{2}$

$EBM=\frac{8.8195-6.9805}{2}$

$EBM=0.9195$.

The confidence interval and error bound will decreases as we see all above .