Question

According to cdc 47% of adults have hypertension. in a random sample of 500 us adults, find the probability that sample the proportion of adults with hypertension is greater than 5.

Answer 1

To find the probability that the sample proportion of adults with hypertension is greater than 5%, we need to use the concept of sampling distribution of proportions. The probability is essentially 0.

Step-by-step explanation:

To find the probability that the sample proportion of adults with hypertension is greater than 5%, we need to use the concept of sampling distribution of proportions. Given that 47% of adults have hypertension according to the CDC, we can assume that the population proportion is 0.47. The standard deviation of the sampling distribution is given by:

sqrt((p * (1-p))/n) = sqrt((0.47 * 0.53)/500) = 0.021

Using the Central Limit Theorem, we can approximate the sampling distribution as a normal distribution. To find the probability that the sample proportion is greater than 5%, we standardize the value:

Z = (0.05 - 0.47)/0.021 = -19.05

Looking up the z-score in a standard normal distribution table or using a calculator, we find that the probability is essentially 0 (very close to 0).