Chebyshev’s Theorem

1. The lengths of pins produced by a machine follow a normal distributionwith mean2.54 cm and standard deviation0.04 cm. A pin is rejected if its length is less than 2.44 cm or more than 2.60 cm.

Find the percentage of pins that are accepted.

2. If it is decided that 2.5% of the pins are to be rejected because they are two long and 2.5% because they are two short, determine the new rangeof acceptable lengths.

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