Question: In an accelerator centre, an experiment needs a 1.41-cmthick aluminium cylinder (http://puhep1.princeton.edu/mumu/ target/Solenoid_Coil.pdf). Suppose that the thickness of a cylinder has a normal distribution with

In an accelerator centre, an experiment needs a 1.41-cmthick aluminium cylinder (http://puhep1.princeton.edu/mumu/ target/Solenoid_Coil.pdf). Suppose that the thickness of a cylinder has a normal distribution with a mean of 1.41 cm and a unknown standard deviation. It is also known that 15.87% of cylinder is greater than 1.42 cm.

a. What is the standard deviation of thickness of a cylinder?

b.If the specifications require that the thickness is between 1.39 cm and 1.43 cm, what proportion of the samples meets specifications?

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