91Ó°ÊÓ

I The sample mean time to complete 100 tax forms is 23.6 hours

$\overline{x}$ $=23.6hours$

ii. Standard deviation of time to complete the tax forms is 7 hours,

$\mathrm{Î\pm }=7$

iii. Number of people who were surveyed for the time to complex tax forms is,

$n=100$

Time completed to form the separate tax form is X and the mean time to complete tax forms from a sample of 100 customers is X

Normal distribution use for the problem. As we know that sample size is more than 30 for the standard deviation of the population n and the distribution is N$\left(\begin{array}{c}23.6,\underline{7.0}\\ \sqrt{100}\end{array}\right)$.

I. State the range of confidence.

CI stands for "Common Interest"

CI= (22.228, 24.972)

ii. The graph is given below,

iii. The error bound is calculated from the formula,

EBM = $\frac{Upperlimit-Iowerlimit}{2}$

EBM = $\frac{24.751-22.440}{2}$

$EBM=1.151$

It is likely that the sample size will need to be adjusted. The firm requires the confidence level to be determined, after which we must use the error bound formula to calculate the required sample size.

Because of the same size error constraint, the confidence level would decrease for the same size interval and likewise for a smaller sample size.

According to the error bound formula, 206 people in the firm needs to be surveyed as the confidence level rises, requiring an increase in the sample size or the error bound.