Problem $2$

Consider the spot speed data here, collected at a rural highway site under

conditions of uncongested flow:

Speed Group $($mi$/$h$)$Number of Vehicles Observed $($N$)$

$15-200$

$20-254$

$25-309$

$30-3518$

$35-4035$

$40-4542$

$45-5032$

$50-5520$

$55-609$

$60-650$

$($a$)$Plot the frequency and cumulative frequency curves for this data.

$($b$)$Determine the median speed, the modal speed, and show how each

was found.

$($c$)$Compute the mean and standard deviation of the speed distribution

$($d$)$What are the confidence bounds of the estimate of the true mean

speed of the distribution with $95\%$confidence$?$ With $99\mathrm{.}7\%$

confidence?

$($e$)$Based on the results of this study, a second is to be conducted to

achieve a tolerance of $0\mathrm{.}8$mi$/$h with $95\%$confidence$.$ What sample

size is required?