According to the Centers for Disease Control and Prevention (CDC) , 47% of adults in the United States have hypertension. In a r

Question

2 years ago

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andom sample of 500 U.S adults, find the probability that sample the proportion of adults with hypertension is greater than 0.5.

1 answer:

harina [27] · Answer 1 · 2023-04-06T12:00:18+03:00

The probability that sample the proportion of adults with hypertension is greater than 0.5 is 0.090

<h3>How to determine the probability?</h3>

The given parameters are:

p = 47%

Sample size, n =500

The standard deviation is calculated as:

$\sigma = \sqrt{np(1 - p)$

So, we have:

$\sigma = \sqrt{500 * 47\%(1 - 47\%)$

Evaluate

σ = 11.16

The number of adults with hypertension is calculated as:

x = 500 * 0.5 = 250

And the mean is:

μ = 500 * 0.47 = 235

Start by calculating the z-score

$z = \frac{x - \mu}{\sigma}$

This gives

$z = \frac{250 - 235}{11.16}$

Evaluate

z = 1.34

The probability is then calculated as:

P(z >1.34) = ??

From z table of probabilities, we have:

P(z >1.34) = 0.090

Hence, the probability that sample the proportion of adults with hypertension is greater than 0.5 is 0.090