2. (25 points) The MTA operates the New York City subway system, and is exploring the idea of adding additional subway trains during rush hour to accommodate the large number of passengers that use the subway. They are interested in the proportion of subway cars during rush hour that are over capacity. Overcapacity is defined as having more than 90 passengers. As a first step, they conduct a simple random sample of 40 subway cars during rush hour and record the number of riders in each car. Out of these 40 cars, they find that 15 are over capacity. We would like to know is the proportion of subway cars in New York City operating over capacity during rush hour different than 50%? (a) (5 points) Check: If we wanted to compute a 90% confidence interval, are the conditions for the central limit theorem met in order to proceed with confidence interval calculations? Explain. (b) (5 points) Calculate: Assuming the conditions for the Central Limit Theorem hold, con- struct a 90% confidence interval for the proportion of subway cars in New York City operating over capacity during rush hour. (Round any numbers in your final answer to 3 decimal places.) (c) (10 points) Conclude: Interpret the confidence interval you found in part b. Can we conclude the proportion of subway cars operating over capacity is different to 50%?