Question

Researchers estimated the prevalence of metabolic syndrome in adults in the united states to be 34%.

a. suppose a sample of 12 adult patients at a clinic is collected. what is the standard deviation?
b. suppose a sample of 10 adult patients at a clinic is collected. what is the standard deviation?
c. suppose a sample of 15 adult patients at a clinic is collected. what is the standard deviation?

Answer 1

The standard deviation for the prevalence of metabolic syndrome in adults using a binomial distribution varies with the sample size: it's approximately 1.638 for 12 patients, 1.495 for 10 patients, and 1.844 for a sample of 15 patients.

Step-by-step explanation:

When calculating the standard deviation for the prevalence of metabolic syndrome in a sample of patients, we make use of the binomial distribution properties. The formula for the standard deviation of a binomial distribution is sqrt(np(1-p)), where n is the sample size and p is the probability of success (in this case, having metabolic syndrome).

In our cases:

• For a sample of 12 adult patients: sqrt(12*0.34*(1-0.34)) = sqrt(12*0.34*0.66) = sqrt(2.68224) ≈ 1.638.
• For a sample of 10 adult patients: sqrt(10*0.34*(1-0.34)) = sqrt(10*0.34*0.66) = sqrt(2.234) ≈ 1.495.
• For a sample of 15 adult patients: sqrt(15*0.34*(1-0.34)) = sqrt(15*0.34*0.66) = sqrt(3.402) ≈ 1.844.

Therefore, the standard deviation varies with the sample size, reflecting the variability in the proportion of patients with metabolic syndrome in each sample.