Question

the national health examination survey reported that in a sample of 13,267 adults, 6634 had high cholesterol (total cholesterol above 200 mg/dl), 8093 were overweight (body mass index above 25), and 4113 were both overweight and had high cholesterol. a person is chosen at random from this study. round all answers to four decimal places. (C) find the probability that the person does not have high cholesterol. The probability that the person does not have high cholesterol is?(D) Find the probability that the person is overweight or has high cholesterol. The probability that the person is overweight or has high cholesterol is?

Answer 1

The results of the National Health Examination Survey are:

High Cholesterol: 6634

Overweight: 8093

Both overweight and had high cholesterol: 4113

Sample size: 13 267

(C)

We need to calculate the probability that the person does not have high cholesterol. To do that, we need to find the probability that the person does have cholesterol, and then subtract this result from 1. Then:

P[not high cholesterol] = 1 - P[high cholesterol]

P[high cholesterol] = (# people that have high cholesterol) / (Total # of people)

P[not high cholesterol] = 1 - (6634) / (13 267) = 0.499962...

Rounding to four decimal places:

P[not high cholesterol] = 0.5000

(D)

Now, we need to calculate the probability that the person is overweight or has high cholesterol. We define the events:

A: The person has high cholesterol

B: The person is overweight

Then:

P[A ∪ B] = P[A] + P[B] - P[A ∩ B]

Where:

P[A] = 6634/13267

P[B] = 8093/13267

P[A ∩ B] = 4113/13267

Where we defined the probability as:

P[C] = (# of events C) / (# of total events)

Then:

P[A ∪ B] = 6634/13267 + 8093/13267 - 4113/13267 = (6634+8093-4113)/13267

P[A ∪ B] = 10614/13267

Rounding to four decimal places:

P[A ∪ B] = 0.8000