3. A variable X follows some left-skewed distribution with mean 100 and standard

Question

3. A variable X follows some left-skewed distribution with mean 100 and standard deviation f 2,500 observations from this distribution and create a 50. We take a random histogram of the data values. We expect the histogram to be: sample o (A) approximately normal with mean close to 100 and standard deviation close to 1. (B) skewed to the left with mean close to 100 and standard deviation close to 1. (C) approximately normal with mean close to 100 and standard deviation close to 50. (D) skewed to the left with mean close to 100 and standard deviation close to 50. (E) approximately normal with mean close to 100 and standard deviation close to 0.02.

Explanation / Answer

Answer is A. See, below

Now, the random sample size is very large. Since the CLT therom says that if sample size is large the distribution will tend to be approximately normal.

So, A, C and E may be right answers, B and D are out.

The mean will always be the same as sample mean i.e. 100

The standard deviation is 50/sqrt(2500) [stdev/sqrt(n)] = 50/sqrt(2500) = 1

So, A is correct, it is only option matching

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