Answer:
a) 151lb.
b) 6.25 lb
Step-by-step explanation:
The Central Limit Theorem estabilishes that, for a random variable X, with mean 
and standard deviation 
, a large sample size can be approximated to a normal distribution with mean and standard deviation 
.
In this problem, we have that:
So
a) The expected value of the sample mean of the weights is 151 lb.
(b) What is the standard deviation of the sampling distribution of the sample mean weight?
This is 
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So, this question is basically asking us "If we had an x instead of a 2, would this be true?" We can try and see what we get:
So, if we want to show this we have to change the numerator or denominator in such a way that we can cancel some common factors. Notice that 
If we replace the factored numerator with the original one, we get:
Since we have an equality, this relation is proved.
