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irinina [24]
3 years ago
11

Suppose the rate of type II diabetes in 40- to 59-year-olds is 7% among Caucasians, 10% among African-Americans, 12% among Hispa

nics, and 5% among Asian-Americans. Also suppose the ethnic distribution for the age group is 30% Caucasian, 25% African-American, 40% Hispanic, and 5% Asian-American. What is the overall probability of type II diabetes among 40- to 59-year-olds in Houston?
Mathematics
1 answer:
melomori [17]3 years ago
4 0

Answer:

The overall probability of type II diabetes among 40- to 59-year-olds in Houston is 9.3%.

Step-by-step explanation:

We have these following rates of type II diabetes:

7% among Caucasians

10% among African-Americans

12% among Hispanics

5% among Asian-Americans.

The ethnic distribution of Houston is:

30% Caucasian

25% African-American

40% Hispanic

5% Asian-American

What is the overall probability of type II diabetes among 40- to 59-year-olds in Houston?

P = P_{1} + P_{2} + P_{3} + P_{4}

P_{1} is the probability of finding a Caucasian with type II diabetes in Houston. So it is 7% of 30%.

P_{1} = 0.07*0.30 = 0.021

P_{2} is the probability of finding an African-American with type II diabetes in Houston. So it is 10% of 25%.

P_{2} = 0.1*0.25 = 0.0215

P_{3} is the probability of finding a Hispanic with type II diabetes in Houston. So it is 12% of 40%.

P_{3} = 0.12*0.40 = 0.048

P_{4} is the probability of finding an Asian-American with type II diabetes in Houston. So it is 5% of 5%.

P_{3} = 0.05*0.05 = 0.0025

P = P_{1} + P_{2} + P_{3} + P_{4} = 0.021 + 0.0215 + 0.048 + 0.0025 = 0.093

The overall probability of type II diabetes among 40- to 59-year-olds in Houston is 9.3%.

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