Question

# The height of women in the US is normally distributed with mean (mu) = 65 inches...

The height of women in the US is normally distributed with mean (mu) = 65 inches and standard deviation (sigma) = 2.5 inches. A random sample of 15 women is chosen from all women in the US. Is the sampling distribution of the sample ( x - bar) mean normally distributed? Why?

 A. No because the standard deviation is too small B. No because x < 30 C. Yes. Because x < 30 D. Yes, because the original x distribution was normally distributed

According to central limit theorem,

i) If distribution of random variable x is normal then the sampling distribution of sample mean is also normally distributed.

ii) If sample size n is large (n > 30) then the sampling distribution of sample mean is approximately normally distributed irrespective of the distribution of random variable x.

Here random variable X is height of women in the US.

X is normally distributed.

So, the sampling distribution of the sample mean is normally distributed.

Option D is correct.

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