Question

Part 2 of 6 Find the probability that more than 42% of the people in this sample have high blood pressure. The probability that more than 42% of the people in this sample have high blood pressure is Blood pressure: 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 0.4. A sample of 40 U.S. adults is chosen. Use the TI-84 Plus Calculator as needed. Round the answer to at least four decimal places. Part 1 of 6 Is it appropriate to use the normal approximation to find the probability that more than 42% of the people in the sample have high blood pressure? It is appropriate to use the normal curve, since np - 16 10 and 1 (1 - p) - 24 10. Part: 1/6 Part 2 of 6 Find the probability that more than 42% of the people in this sample have high blood pressure. The probability that more than 42% of the people in this sample have high blood pressure is

Answer 1

To find the probability that more than 42% of the people in the sample have high blood pressure, you can use the normal approximation. The probability is very close to 0.

Step-by-step explanation:

To find the probability that more than 42% of the people in the sample have high blood pressure, we can use the normal approximation. We are given that the proportion of U.S. adults with high blood pressure is 0.4 (40%).

To use the normal approximation, we need to check if the conditions are met. The conditions are:

The sample is a simple random sample.

The sample size is large (n >= 10) and the population is at least 10 times the size of the sample.

The observations in the sample are independent.

We need to calculate the mean and standard deviation of the sample proportion. The mean (mu) of the sample proportion is given by np, where n is the sample size and p is the proportion of success (high blood pressure).

In this case, the sample size is 40 and the proportion of high blood pressure is 0.4. So the mean is mu = 40 * 0.4 = 16.

The standard deviation (sigma) of the sample proportion is given by sqrt(np(1-p)). In this case, the standard deviation is sigma = sqrt(40 * 0.4 * (1-0.4)) = 3.2.

Now, we can use the normal distribution to find the probability that more than 42% of the people in the sample have high blood pressure.

First, we need to convert the proportion of 42% to a z-score using the formula z = (x - mu) / sigma, where x is the value we are interested in (42 in this case). So the z-score is z = (42 - 16) / 3.2 = 8.125.

Next, we can use a standard normal distribution table or a calculator to find the probability corresponding to the z-score. On a TI-84 Plus Calculator, you can use the command '1 - normalcdf(-10^99, 8.125)'. This will give you the probability of getting a z-score greater than 8.125, which is approximately 0. As a result, the probability that more than 42% of the people in this sample have high blood pressure is very close to 0.

Answer 2

To find the probability that more than 42% of the people in the sample have high blood pressure, you can use the normal approximation. Calculate the mean and standard deviation for the sample proportion, find the z-score for the desired proportion, and use a z-table or calculator to find the probability. Subtract the probability from 1 to find the desired probability.

Step-by-step explanation:

To find the probability that more than 42% of the people in the sample have high blood pressure, we need to use the normal approximation. Since the sample size is large (n = 40) and the sample proportion is not too close to 0 or 1, the normal approximation is appropriate.

First, calculate the mean and standard deviation for the sample proportion. The mean is np = 40(0.4) = 16 and the standard deviation is √(np(1-p)) = √(40(0.4)(1-0.4)) ≈ 3.20.

Next, calculate the z-score for the desired proportion. The z-score is (x - mean) / standard deviation, where x is the desired proportion. In this case, x = 0.42.

Using the formula (0.42 - 0.4) / 0.32 = 0.020 / 0.32 = 0.0625, we can find the z-score.

Using a z-table or calculator, we can find the probability corresponding to the z-score. Since we want the probability that more than 42% of the people have high blood pressure, we need to find the area to the right of the z-score.

Finally, subtract the probability from 1 to find the desired probability.

The probability that more than 42% of the sample has high blood pressure is the area to the right of 0.65 under the standard normal curve. Using the z-table or calculator again, we find this area to be approximately 0.2578.

Therefore, the probability that more than 42% of the people in this sample have high blood pressure is approximately 0.2578, rounded to four decimal places.