1. A small, independent amusement park collects data on the number of cars with outof-state license plates. The sample size is fixed at n=25 each day. Data from the previous 10 days indicate the following number of out-of-state license plates: [10 Points] (a) Calculate the overall proportion of "tourists" (cars with out-of-state plates) and the standard deviation of proportions. (b) Using a 95.45% confidence, calculate the LCL and UCL for these data. (c) Draw the control chart? (d) Is the process under control? Explain why. (e) What type of variation is present? 2. A toy manufacturer has three different mechanisms that can be installed in a doll that it sells. The different mechanisms have three different setup costs (overheads) and variable costs and, therefore, the profit from the dolls is dependent on the volume of sales. The anticipated payoffs are as follows. [15 Points] a. Use the Maximax, Maximin, and Equally Likely criterion to determine the best alternative? b. Calculate the EMV for each decision alternative? b. Which action should be selected? c. What is the expected value with perfect information? d. What is the expected value of perfect information