# Coil Probability

**Paper, Order, or Assignment Requirements**

A composite heater consists of two identical coils. The total thermal output desired from the heater is 1000 kW. The two identical coils generate equal output to meet these requirements. The Mean Time to Failure of a heating coil can be modelled using the normal distribution with a mean of 22 months and a standard deviation of 10 months. The heater is said to have a total failure when all the coils fail. If one coil fails and the other is still working, the working coil will keep generating its design heat output. The heater is said to be at least partially functional if it generates at least 50% of the desired output.

1. Determine the probability that the heater will have a total failure within 25 months

2. Determine the probability that the heater will generate at least 500 kW of thermal energy after 20 months.

3. Now consider a scenario where the heater may consist of a general ‘n’ number of identical coils to generate the desired output. What is the probability that the heater will be at least partially functional after 25 months for n = 1, 2, 3, 4, and 5?

Please show all your steps clearly

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