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

Answer:

c) 75, 2

Step-by-step 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 $\frac{\sigma}{\sqrt{n}}$.

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 $\mu = 75, s = \frac{16}{\sqrt{64}} = 2$.

So the correct answer is:

c) 75, 2