The highway department wants to estimate the proportion of vehicles on Ontario’s Highway 401 between the hours of midnight and 5 a.m. that are 18-wheel tractor trailers. The estimate will be used to determine highway repair and construction considerations and in highway patrol planning. Suppose analysts for the highway department counted vehicles at different locations on the highway for several nights during this time period. Of the 3,481 vehicles counted, 927 were 18-wheelers.

a. Determine the point estimate for the proportion of vehicles travelling Highway 401 during this time period that are 18-wheelers.

b. Construct a 99% confidence interval for the proportion of vehicles on Highway 401 during this time period that are 18-wheelers.