a) Explain briefly what this means in practice that the lengthof the pipes is expected to be µ = 12. What is the probability thata randomly selected pipe is longer than 12.2 meters? What is theprobability that the length of a randomly selected pipe is between11.9 and 12.1 meters? What length is 90% of the tubes longer than?The company has been commissioned to produce a 10.8 kilometer (ie10800 meters) long pipeline. The has a margin of error of ± 5meters, that is, they can deliver a pipeline that is up to 5 metersshorter or 5 meters longer than the specified length of 10800meters. The company is thinking of producing 900 pipes to thepipeline, and the total length of the pipeline then becomes the sumof the lengths of these pipes. Suppose each tube produced by themachine to the company has a length that is independent of theothers tubes. b) What is the expected total length of the pipeline?What is the variance of the total length? What is the probabilitythat the pipeline will be too long or too short (ie get a lengthbeyond the allowed margin of error)? If the standard deviation ofthe lengths of the pipes, ?, could be adjusted to a differentvalue, which value had to be adjusted so that the likelihood of thepipeline becoming too long or too long card to be 0.01? Beforeproduction is fully commissioned, one of the engineers at thecompany insists that they have to examine if the machine isproperly adjusted so that the expected length of the pipes isreally 12 meters. To examine this, they produce 12 tubes andmeasure their length. The results of the measurements are givenbelow. We assume in the rest of the task that µ is unknown, whilewe still have that ? = 0.1 and that the lengths of different pipesare independent. M?aleresultater: 11.87 11.82 11.99 12.01 11.9311.98 12.08 12.11 11.92 11.79 12.02 12.07 c) Calculate the mean andmedian of the data. Find a 95% confidence interval for µ. How manymeasurements must be made in this situation at least