Cholesterol levels among fourteen-year-old boys are roughly...

Cholesterol levels among fourteen-year-old boys are roughly Normal, with mean 172 and standard deviation 30 milligrams per deciliter (mg/dl). Researchers choose an SRS of 100 fourteen-year-old boys and average their cholesterol levels. Estimate the probability that the sample mean is 180mg/dl or more by assuming that the sampling distribution is approximately Normal. It was reported that 40% of population in a certain country have blood type O. We plan to take a random sample of 121 medical records. What is the standard deviation of the sampling distribution of the sample proportion of blood type O?

Transcript

00:01 All right, in your question, we are told that we have these cholesterol levels.

00:04 There's two questions here.

00:05 Cholesterol levels among 14 -year -old boys, you're told that it's roughly normal with the mean of 172 and a standard deviation of 30.

00:14 Researcher chose a simple random sample of 100.

00:18 I said let x bar stand for the sample mean, and that's what we're looking for.

00:23 What's the probability that a sample mean from that 100 has a blood pressure? reading or i'm sorry a cholesterol reading of 180 or 180 or higher so what we want to figure out first is we want to find the standard deviation of our sampling distribution of sample means and that formula is to take your population standard deviation divided by the square root of your sample size so for us that would be 30 divided by the square root of 100 which is 30 divided by 10 or 3 then what we could do we could find a z score for the sample in question and that is found by taking x bar minus the mean divided by our standard deviation or sampling distribution so that's going to work out to 180 minus 172 over 3 which is 8 divided by 3 which i'll just leave at 8 3rd you could change it to a decimal two but it's going to be 2 .6 repeating.

01:39 Now i'd like to draw out what we're looking for here.

01:45 On our normal model, our mean for this sample, i'm sorry, for this question is 172, and we have a sample mean of 180 we're looking for seeing if we have a probability being that much or higher.

02:00 So we want the probability here.

02:02 You could take this value to a z table and estimate, and what a z table would show you as the area to the left of that boundary, and you would have to take one minus that area.

02:15 I'm going to do this using technology, using normal cdf, and i don't even need to use my z score if i use technology.

02:25 I could, so i guess i will.

02:28 It'll be eight -third is our z score at that location.

02:33 Your upper boundary, you just want to put in a big number, like a million, because we're heading off this direction to infinity...

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