An HP laser printer is advertised to print text documents at a speed of 23 ppm (pages per minute). The manufacturer tells you that the printing speed is actually a Normal random variable with a mean of 22.49 ppm and a standard deviation of 4.15 ppm. Suppose that you draw a random sample of 43 printers.
Part i) Using the information about the distribution of the printing speeds given by the manufacturer, find the probability that the mean printing speed of the sample is greater than 23.19 ppm. (Please carry answers to at least six decimal places in intermediate steps. Give your final answer to the nearest three decimal places. Use Rcmdr for this question.)
Part ii) Use normal approximation to find the probability that more than 47% of the sampled printers operate at the advertised speed, i.e. the printing speed is equal to or greater than 23 ppm. (Please carry answers to at least six decimal places in intermediate steps. Give your final answer to the nearest three decimal places. Use Rcmdr for this question.)