1). The bicycle manufacturer imports chains from the company CHX. The average life of the chains is 1500 km and have a standard deviation of 433 km. CHX randomly selects 100 chains. What is the probability that the mean life of this 100 chains is less than 1431 km?

2). The company CRAN produces crankshafts for automobile engines. The average life of the crankshafts is 22980 km and the standard deviation is 365 km. The company CRAN has developed a new bearing coating and claims that the average life of the crankshaft has increased. Therefore, he randomly selects 36 crankshafts and carries out experiments. The average life of the tested crankshafts is 23108 km. Is there an evidence of α=0,05 that the life of the crankshaft has increased?

3). The company Wings produces shafts by using 7075 aluminum. The company claims that 96% of the produced shafts have no defects (non-defective). We randomly select 150 shafts. What is the probability that the randomly selected 150 shafts are 97-99 % non-defective?

4). The effective life of a piston used in an automobile is a random variable with mean 8695 kilometers and standard deviation 100 kilometers. The distribution of effective life is fairly close to a normal distribution. The engine manufacturer introduces an improvement into the manufacturing process for the pistons that increases the mean life to 8785 kilometers and decreases the standard deviation to 87 kilometers. Suppose that a random sample of n1 pistons is selected from the old process and a random sample of n2 45 pistons is selected from the improved process. What is the probability that the difference in the two pistons mean x1 – x2 is at least 50 kilometers?