As part of an overall evaluation of training methods, an experiment was conducted to determine the average exercise capacity of healthy male army inductees. to do this, each male in a random sample of 35 healthy army inductees exercised on a bicycle ergometer (a device for measuring work done by the muscles) under a fixed work load until he tired. blood pressure, pulse rates, and other indicators were carefully monitored to ensure that no ones health was in danger. the exercise capacities (mean times measured in minutes) for the 35 inductees yielded the sample mean of 31.51 minutes. the historical records show that the standard deviation for an individual inductee’s exercise capacity is 12.4 minutes.(a) in one or two sentences, explain whether or not it is reasonable to assume that the sampling distribution of the sample mean exercise capacity time is approximately normal.(b) in past such studies, the average exercise capacity was 30 minutes. suppose the researchers wanted to test whether the average exercise capacity has changed from the historical average. test the researcher’s assertion using ? = 0.05. clearly define the parameter in this test and state the hypotheses in terms of this parameter.(c) would 30 minutes fall inside the 95% confidence interval for the average exercise capacity using the same data? explain your reasoning in one sentence, without actually computing the interval.