Question

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 2.5 cm with a standard deviation 0.2 cm. 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 cm, 7.2 cm
b. 36 cm, 1.2 cm
c. 90 cm, 2.7 cm
d. 90 cm, 1.2 cm
e. 36 cm, 7.2 cm

Answer 1

d. 90 cm, 1.2 cm

Explanation:

Given that:

The sample size n = 36

For the length of the link:

The mean
`\overline x` = 2.5

The standard deviation s = 0.2 cm

In a chosen 36 links, The mean and standard deviation for the length chain is as follows:

Mean = n
`\overline x`

Mean = 36×2.5

Mean = 90 cm

The Standard deviation = s×√n

The Standard deviation = 0.2×√36

The Standard deviation = 0.2×6

The Standard deviation = 1.2 cm