c) Your analysis shows that the mean resistance of a batch of 500 of the resistors you have selected is 21.5k(, with a standard deviation of 2k(. Assuming the resistors are normally distributed, determine the number of resistors likely to have values between 19k( and 24kQ. Note: Use the z-table given in Appendix A when answering part c. d) The Quality Assurance Department is anxious to improve the nominal value of the resistors to ensure more of them fall within the rated tolerance band. The manufacturing process is adjusted in an attempt to bring about this improvement. Following the adjustment, a further sample of 100 resistors is taken in order to determine if the adjustment has resulted in an improvement to the nominal value of the resistors. Analysing this second sample, it is noted that the mean value is now 21.8kQ, with a standard deviation of 1k(. By comparing these new results of the resistor values following the manufacturing adjustment, with the values obtained in part (c) recorded before the adjustment, show whether or not you agree with the hypothesis that the adjustment to the manufacturing process has had a beneficial effect by making the resistor values closer to the desired manufactured nominal value of 22k(. Illustrate your answer with a hand drawn sketch of the normal distribution, with shaded regions representing the results of your analysis, which you can show to the Quality Assurance Manager. Note: Use the z-table given in Appendix A when answering part d.\f