The diameter of a case hardened axle is normally distributed…

The diameter of a case hardened axle is normally distributed with a mean of 1.5 inches with a standard deviation of 0.007 inches.  a) If we know the tolerance on axle thickness is ±0.011 inches, what percentage of axles produced will fall out of tolerance. b) If we randomly select 4 axles, what is the probability that the mean thickness is within tolerance?  c) Suppose we allow the axle manufacturing to continue over a month.  At the end of the month if we randomly sampled 4 axles and found a mean thickness of 1.508 inches can we say this occurrence can be expected?  Explain fully using probability to support your claim.  

An employee at a local tool supply store wants to convince c…

An employee at a local tool supply store wants to convince customers that the local budget tool is just as consistent as the reputable name brand tools.  The employee cut a length of aluminum stock to 2 inches in length and then randomly selected 10 name brand tools and 10 budget tools to measure the cut length.  The sample information below summarizes the findings of the experiment.  You may assume the measurements follow a normal distribution. Construct a 99% interval estimate for the ratio of the variance in measurement for these tools.  Is there reason to believe that the employee is correct in their claims?  Explain.