# Math Help - Normal distribution problem

1. ## Normal distribution problem

The cholesterol levels of adult women can be described by a normal distribution
with a mean of 184 mg/dL and a standard deviation of 24.

For a group of 36 women, what is the probability that the average cholesterol
level of the group is greater than 190 mg/dL?

I can handle normal distribution problems in general. But I dont know how to deal with this one where it is asking about a group of people and getting their average cholesterol?

2. ## Re: Normal distribution problem

You are considering a sample of 36 women here, so the average mean will still be 184 mg/dL (you can see that the weight of each woman is normal with a mean of 184, so the central limit theorem tells us the mean of the sample will be 184), however the variance will decrease linearly with the sample size. Your new standard deviation is therefore $\frac{24}{\sqrt{36}} = 4$ (since variance is standard deviation squared).

Now you can use the your probability density function as usual, with mean 184 and standard deviation 4, to obtain the correct probability.

This makes sense if you consider larger and larger samples - as the number of women sampled increases, it's more and more likely that the mean of the group will be 184, so the probability that the average weight is above 190 should decrease - which is correctly reflected in mathematics in that the standard deviation tends to zero