An engineer wishes to estimate the average speed on a roadway at a $95\%$ confidence level so that the estimate is within $2$ mi$/$h of the true average. He collects $50$ spot speed observations.After analyzing the collected data, he realizes that the standard deviation of the data is $5\mathrm{.}0$ mi$/$h$.$a$)$ Is the number of collected data sufficient? b$)$ What is the estimate of the error based on the actual number of collected data?