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In a mechanical engineering laboratory, a stress test is performed on a batch of 100 identical steel rods. The stress values (in megapascals, MPa) observed for these rod: are recorded and found to be normally distributed with a mean () of 75MPa and a standard deviation () of 5MPa. A failure is defined as any rod with a stress value below 70MPa. Calculate the probability that: 1. Exactly 10 rods out of the 100 rods will fail the stress test. 2. More than 15 rods will fail the stress test. 3. The average stress value of a random sample of 20 rods from this batch is less than 72MPa. Here are the new input data ( 100 stress values): data =[74.5,77.1,72.3,73.8,75.5,78.2,76.4,74.9,76.8,73.2, 75.7,75.1,76.0,74.6,73.9,75.3,72.9,76.7,73.5,77.5, 74.8,76.3,75.2,73.7,77.0,74.4,75.9,73.0,76.5,74.7, 72.8,73.6,76.6,75.6,74.2,77.3,73.3,75.4,76.9,72.7, 74.1,76.1,75.0,77.4,73.1,75.8,74.0,76.2,77.2,72.6, 73.4,75.0,74.7,76.4,72.5,76.1,73.9,75.5,74.3,76.2, 73.6,75.2,77.0,74.0,76.3,72.4,73.8,75.7,74.6,76.8, 72.3,75.4,74.2,76.9,73.7,75.3,74.5,76.0,73.5,77.5, 72.2,75.1,74.4,77.3,73.4,76.5,74.1,75.9,72.1,76.6, 73.3,74.9,75.8,77.2,73.2,76.7,72.0,74.8,75.6,74.3, 76.7,72.1,74.4,75.0,73.9,76.4,72.2,74.5,75.1,74.0]