Sometimes The ma- Introduction to Statistics and Data Analysis (4 problems) Problem 1 - Descriptive statistics and graphical analysis. A quality-control engineer records the number of defects observed on 30 randomly selected printed circuit boards (PCBs): `5, 2, 3, 4, 7, 1, 6, 3, 4, 2, 9, 3, 5, 2, 4, 4, 5, 2, 3, 6, 8, 5, 3, 2, 4, 5, 7, 3, 4, 6`. (a) Compute the sample mean, median, mode and sample variance of the defect counts. Interpret each measure in the context of PCB quality. (b) Construct a frequency table and histogram for the defect counts using appropriate class intervals. Identify whether the distribution is symmetric, positively skewed or negatively skewed. (c) Prepare a box-and-whisker plot of the data. Identify any potential outliers using the 1.5IQR rule and discuss what they might indicate. (d) If the process mean and standard deviation from historical data are 4 defects and 2 defects respectively, compute the z-scores for each observation and determine how many PCBs fall within 1 standard deviation of the mean. Compare this proportion with the empirical rule.nagerial decision-making process involves making _______ among relevant considerations, of which ethical considerations are only one type. encounter serious difficulties