A sensor unit (in fact, a digital scale, shown in the picture below) is programmed to send a data packet (containing the weight measurement at the moment) every 100 milliseconds (ms) to the main computer console via a serial port. Upon receiving each data packet, the computer console logs the current timestamp along with the received data. For subsequent analysis, multiple channels of sensory data will be aligned by their timestamps to form a multivariate time series dataset. Therefore, it is critical to verify that the actual rate at which the sensor unit sends data packets conforms to what is set in the control program, and to quantify the variability in the time elapsed between successive data packets. A precision level of 0.1 ms is needed for the analysis.

Apply necessary data processing steps (e.g., converting the timestamps to milliseconds, take the difference between successive timestamps to get the time interval, etc.) on the sample data, to make it suitable for analysis. Formulate and solve appropriate statistical inference problems (e.g., point estimation, confidence interval or hypothesis testing, Goodness-of-fit tests, etc.) to answer these questions: 1. What is the estimated standard deviation of the actual inter-sending time (defined as the number of milliseconds elapsed per data packet sent)? 2. Is Normal distribution a good population model for the sensor's actual inter-sending time? 3. Does the sensor's inter-sending time conform to what is specified in the program (i.e., 100 ms)?