Answer:
The approximated value of the standard deviation is 0.35.
Step-by-step explanation:
According to the Central Limit Theorem if we have an unknown population with mean <em>μ</em> and standard deviation <em>σ</em> and appropriately huge random samples (<em>n</em> > 30) are selected from the population with replacement, then the distribution of the sample mean will be approximately normally distributed.
Then, the mean of the distribution of sample means is given by,
And the standard deviation of the distribution of sample means is given by,
The information provided is:
<em>n</em> = 100
<em>σ</em> = 3.5
<em>μ</em> = 66
As the sample size is quite large, i.e. <em>n</em> = 100 > 30, the central limit theorem can be applied to approximate the sampling distribution of sample mean by the Normal distribution.
Then the approximated value of the standard deviation of sampling distribution of sample mean is:
Thus, the approximated value of the standard deviation is 0.35.