Consider a manufacturing process called as turning (a type of machining process) that is used to manufacture cylindrical metal samples with a nominal diameter of 10.00 mm. past data from the manufacturer shows a variation in the diameter of samples that is given by a normal distribution with a standard deviation of 0.50 mm. if the specified tolerance on the diameter is 0.75 mm, roughly what percentage of samples manufactured using this process satisfy the tolerance specification?

86.64%

Step-by-step explanation:

Let x be a random variable that represents the diameter of metal samples.

Given : Population mean :

Standard deviation:

Specified tolerance on the diameter is 0.75 mm.

i.e. range of diameter = 10-0.75< x <10+0.75 = 9.25< x< 10.75

Formula to find the z-score corresponds to x:

At x= 0.75,  

Using standard normal table for z-value,

P-value :

∴ Percentage of samples manufactured using this process satisfy the tolerance specification = 86.64%

step-by-step explanation:

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see attached graph