The operations manager at a factory is interested in the lifespan of an electronic component used in one of the factory's machines. The producer of the electronic component claims that it has an average life of 6,200 hours. A random sample of 40 components is studied, and their life spans recorded.
What is the probability of getting a sample result as low as this if the average life of the component is actually 6,200 hours, as the component's producer claims? Does this sample provide evidence that component lifespan is less than the producer claims? You may assume the population standard deviation is equal to the sample standard deviation.