A length of chain is to be constructed by placing 36 component links end to end.The length of a link produced by a production process is known to be a random variable with a mean of $\mu$= 2.5 centimeters and a standard deviation of $\sigma$= 0.2 centimeters.The 36 links are chosen at random from this process to produce the chain.The mean and standard deviation of the length of chain are,respectively,_________.
A)90 centimeters and 7.2 centimeters
B)36 centimeters and 1.2 centimeters
C)90 centimeters and 2.7 centimeters
D)90 centimeters and 1.2 centimeters
E)36 centimeters and 7.2 centimeters

Question

Quizplus · Accepted Answer

The mean length of the chain is the sum of the means of its 36 links, which is $36 \times 2.5 = 90$ centimeters. The standard deviation of the length of the chain, due to the central limit theorem and properties of variance, is the standard deviation of one link times the square root of the number of links, which is $0.2 \times \sqrt{36} = 0.2 \times 6 = 1.2$ centimeters.

A Length of Chain Is to Be Constructed by Placing μ\muμ

A Length of Chain Is to Be Constructed by Placing $\mu$