Question

One truck from lakeland trucking inc can carry a load of 5068.8 lb. Records show that the weights of boxes that it carries have a mean of 75 lb and a standard deviation of 16 lb. For sample size of 64, find the mean and standard deviation of x bar.

a) mean x(bar) =2, standard deviation of x(bar) = 75
b) 16, 75
c) 75, 2
d) 75, 16

Answer 1

c) 75, 2

Explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean
`\mu` and standard deviation
`\sigma`, the sampling distribution of the sample mean, with a large sample size, can be approximated to a normal distribution with mean
`\mu` and standard deviation
`(\sigma)/(√(n))`.

In this problem, we have that:

Records show that the weights of boxes that it carries have a mean of 75 lb and a standard deviation of 16 lb. This means that
`\mu = 75, \sigma = 16`.

For sample size of 64, find the mean and standard deviation of x bar

We have that
`\mu = 75, s = (16)/(√(64)) = 2`.

So the correct answer is:

c) 75, 2