Problem $1.$ Following traffic volumes $(ve\frac{h}{h})$ were recorded for an eastbound section of freeway during the peak hour.

$1850,1900,2100,2075,2110,1975,1990,2055.$

The section has the following characteristics: two $12$ ft wide lanes, $5$ ft lateral shoulder, $10\%$ trucks, rolling terrain, no RVs$.$ PHF $=0\mathrm{.}90.$

$($a$)$ What is the $95\%$ confidence interval $($upper and lower bounds$)$ of the true mean peak hour flow rate of the section during the peak hour?

$($b$)$ What is the $95\%$ confidence interval $($upper and lower bounds$)$ of the peak hour demand flow rate?

$($c$)$ What is the level of service $($LOS$)$ of the section of the highway corresponding to the average peak hour demand flow rates?

$($d$)$ What is the level of service $($LOS$)$ of the section of the highway corresponding to the upper and lower bound of the peak hour demand flow rates?

$($e$)$ What is the probability that the peak hour demand flow rate will exceed the maximum allowed demand flow rate under the current LOS determined in $($c$)?$

Assume that the demand flow rate is normal distributed.