High blood pressure has been identified as a risk factor for...

High blood pressure has been identified as a risk factor for heart attacks and strokes. The proportion of U.S. adults with high blood pressure is 0.35. A sample of 44 U.S. adults is chosen. a) Is it appropriate to use the normal approximation to find the probability that more than 55% of the people in the sample have high blood pressure? b) What is the probability that more than 55% of the people in the sample have high blood pressure? Round to four decimal places.

Transcript

00:01 We are told the proportion of us adults with high blood pressure is 0 .35.

00:05 So it would be p, the population proportion.

00:09 We pick 44 us adults.

00:12 We want the probability more than 55 % of them have high blood pressure.

00:16 Can we use a normal approximation here? so currently this is binomial.

00:21 44 independent trials, two outcomes, high blood pressure or not, same probability for each.

00:29 Can we take a normal approximation? well the requirements to take a normal approximation to the binomial is you need np to be greater than 5.

00:40 You need nq which is 1 minus p to be greater than 5.

00:44 Are those met here? well 0 .35 times 44 is 15 point something.

00:49 So yes we can use a normal approximation.

00:54 Let's do that.

00:56 So a normal distribution has a mean and a standard deviation.

00:59 The mean of a binomial is np, the standard deviation root npq.

01:07 But what i'm actually going to do here is look at proportions since we are looking at 55 % rather than a strict number of people.

01:17 So to turn this from number with high blood pressure to proportion with high blood pressure i'm just going to divide both of these by n.

01:24 That will take me from x, the number with high blood pressure, to x over n, the proportion with high blood pressure.

01:32 So this turns this into a sampling distribution.

01:36 The sampling distribution of p hat, the sample proportion...

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