Please answer these questions in the text box below. All questions share the same context. Please write down the Excel or mathematical formula and the calculated result, keeping a few significant digits. For example: SQRT(10)=3.16. You may also accompany your answers with brief explanations for ease of understanding. 1. A theater uses incandescent bulbs for lighting. A bulb's life has an exponential distribution with a mean of 1200 hours. All bulbs are scheduled to be replaced every 100 hours. What is the chance that a bulb goes out before being replaced? 2. Regardless of the bulb reliability you calculated above, suppose the bulb reliability (not going out before replaced) is 95%. The theater's main lighting module utilizes the following setup: there are four spotlights, each utilizing two parallel (independently wired) bulbs. The lighting module is considered to be in working order if all four spotlights are lit (regardless of one or two lit bulbs). What is the reliability of the main lighting module? 3. A supplier regularly ships spare bulbs in bulk to the theater and promises a 95% reliability (lasting at least 100 hours). The theater inspects each incoming shipment of bulbs by lighting 20 bulbs for 100 hours. If two or more bulbs go out during the test, the batch shipment is returned to the supplier. If the bulbs indeed have a 95% reliability, what is the likelihood that a shipment passes the test