Question 1073724
calculator used can be found at this link:


<a href = "http://davidmlane.com/hyperstat/z_table.html" target = "_blank">http://davidmlane.com/hyperstat/z_table.html</a>


mean = 3.5 years = 42 months
standard deviation = 1 year - 12 months
guaranteed for 12 months.
approximately .62% of the machines will fail within the first 12 months.


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mean = 2 years = 24 months
standard deviation = 1.5 years = 18 months
guaranteed for 6 months.
approximately 15.87% of the machines will fail within the first 6 months.


<img src = "http://theo.x10hosting.com/2017/032102.jpg" alt="$$$" </>


this calculator allows you to use raw scores or z-scores.


z-score = (x-m)/s


x is the raw score.
m is the mean raw score.
s is the standard deviation.


for the first problem:


x = 12
m = 42
s = 12


z = (12 - 42) / 12 = 30 / 12 = -2.5


from the z-score tables, the area under the distribution curve to the left of a z-score of -2.5 will be .0062 = .62%.


same answer.


z-score table used can be found at:


<ahref= "http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf" target = "_blank">http://www.stat.ufl.edu/~athienit/Tables/Ztable.pdf</a>


use of the lane normal distribution calculator will provide the same result as shown below:


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