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.

Medical researchers have developed a new artificial heart co…

Medical researchers have developed a new artificial heart constructed primarily of titanium and plastic. The heart will last and operate almost indefinitely once it is implanted in the patient’s body, but the battery pack needs to be recharged about every 4.5 hours. A random sample of 36 battery packs is selected and subjected to a life test. The average life of these batteries is 4.027 hours. Assume that battery life is normally distributed with standard deviation σ= 0.24 hour.  Is there evidence to support the claim that mean battery life fails to meet the stated life? Use α= 0.01

A recent batch of newly milled parts was sampled from to det…

A recent batch of newly milled parts was sampled from to determine if a majority of the parts needed to be reworked.  The sample consisted of 125 parts, of those sampled 80 were found to need reworking.  Perform a complete test of hypotheses to determine if there is a majority of parts in need of rework.  Use  α=0.10{“version”:”1.1″,”math”:”α=0.10″} for the test.  If there really is no majority, have we committed an error?  Explain fully.