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A study surveys a random sample of 1500 college students from Columbus State University on whether or not they have Type I Diabetes. On the day of the survey, 4 students report that they do have Type I Diabetes.

The prevalence of Type I Diabetes is:
A. [tex]\left( \frac{1500+4}{100} \right) = 15.04\%[/tex]
B. [tex]\left( \frac{100}{1500} \right) + 4 = 4.07\%[/tex]
C. [tex]\left( \frac{4}{1500} \right) \times 100 = 0.27\%[/tex]
D. [tex]\left( \frac{1500}{4} \right) / 100 = 3.75\%[/tex]

Sagot :

GinnyAnsweridn
Sure, let's carefully solve this step by step.

1. Total number of college students surveyed: 1500
2. Number of students reporting Type I Diabetes: 4

To find the prevalence of Type I Diabetes, we need to determine the proportion of students with Type I Diabetes out of the total number surveyed and then convert this proportion to a percentage.

First, calculate the proportion:
[tex]\[ \text{Proportion} = \frac{4 \text{ (students with Type I Diabetes)}}{1500 \text{ (total students)}} = \frac{4}{1500} \][/tex]

Next, convert this proportion to a percentage by multiplying by 100:
[tex]\[ \text{Prevalence (in percentage)} = \left(\frac{4}{1500}\right) \times 100 \][/tex]

Performing the division and multiplication:
[tex]\[ \left(\frac{4}{1500}\right) \times 100 \approx 0.26666666666666666 \% \][/tex]

Rounding to two decimal places, the prevalence is:
[tex]\[ 0.27 \% \][/tex]

So the correct answer is:
[tex]\[ \boxed{(4 / 1500) * 100=0.27\%} \][/tex]
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