Please do not give solution in image formate thanku  When a chip fabrication facility is operating normally, the lifetime of a microchip operated at temperature T, measured in degrees Celsius, is given by an exponential (λ) random variable X with expected value E[X] = 1/λ = (200/T)2 years. Occasionally, the chip fabrication plant has contamination problems and the chips tend to fail much more rapidly. To test for contamination problems, each day 1000 chips are subjected to a one-day test at T = 100C. (a) The probability of more than 2 chips failed in a one-day test (b) Based on the number N of chips that fail in one day, design a significance test for the null hypothesis test H0 that the plant is operating normally at the significance

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When a chip fabrication facility is operating normally, the lifetime of a microchip operated at temperature T, measured in degrees Celsius, is given by an exponential (λ) random variable X with expected value E[X] = 1/λ = (200/T)2 years. Occasionally, the chip fabrication plant has contamination problems and the chips tend to fail much more rapidly. To test for contamination problems, each day 1000 chips are subjected to a one-day test at T = 100C. (a) The probability of more than 2 chips failed in a one-day test (b) Based on the number N of chips that fail in one day, design a significance test for the null hypothesis test H0 that the plant is operating normally at the significance level is α = 0.01 using the following (1) Chebyshev inequality; (2) Central limit theorem

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