Example 3.10 The length of a coil of copper wire is a random variable with mean

Question

Example 3.10 The length of a coil of copper wire is a random variable with mean 150 meters and standard deviation 7 meters. (a) If we choose five coils of wire at random, what is the mean and variance of the average length of these five coils of copper wire? (b) If we choose fifty coils of wire at random, how likely will the average length of copper wire lie between 149 and 151 meters? (c) For fifty coils of wire, find out the length that 90% average length values will be smaller than. I need explanation how to solve this question.

Explanation / Answer

Let X be the length of a coil of copper wire

mu = 150 and std dev = 7 m

a) When sample size = 5,

Mean = 150 and std dev of sample = 7/rt n = 3.130

b) n = 50

Std dev = 7/rt 50 = 0.9900

X=149 implies z = -1/0.99 = -1.01

x =151 z = 1.01

P(149<x<151) = P(|z|<1.01)

=0.6876

c) n =50

P(Z<c) = 0.90

c =1.28

x = 150+1.28(0.9900)

= 151.2672

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