Answer:
The correct option is (a).
Step-by-step explanation:
According to the Central Limit Theorem if we have a population with mean μ and standard deviation σ and take appropriately huge random-samples (n > 30) from the population with replacement, then the distribution of the sample- means will be approximately normally-distributed.
Then, the mean of the sample means is given by,
And the standard deviation of the sample means is given by,
The information provided is:
<em>n</em> = 200
<em>σ</em> = 19.0
Population is skewed.
As the sample selected is quite large, i.e. <em>n</em> = 200 > 30 the central limit theorem can be used to approximate the distribution of the sample mean by the normal distribution.
So, .
Then to construct a confidence interval for mean we will use a <em>z</em>-interval.
And for 95% confidence level we will compute the critical value of <em>z</em>, i.e. .
Thus, the correct option is (a).