Problem #2. ARAlifestyle.com-Do you feel tired all day, even if you slept a full
ID: 3050088 • Letter: P
Question
Problem #2. ARAlifestyle.com-Do you feel tired all day, even if you slept a full8 hours? Do you sufer from unexplained headaches, high blood pressure, cardiac problems and excessive daytime sleepiness? Believe it or not, all your problems could stem from snoring. Snoring is more than just bothersome, it can be hazardous to your health. That's because snoring is the most common symptom of obstructive sleep apnea (OSA), a condition that literally causes you to stop breathing a multitude of times at night. And you often aren't even aware it's happening Scientific American-Data from the Wisconsin Sleep Cohort Study found that 45 percent of all men surveyed and 30 percent of all women surveyed were habitual snorers. Overall, 4 percent of these men and 2 percent of these women had snoring that was associated with obstructive sleep apnea In a sample of 18 area households: What is the probability that at least 3 men snore? a) b) What is the probability that none of the men snore? c) What is the probability that fewer than 13 women snore? d) What is the probability that 7, 8, 9, or 10 women who snore? e) What is the probability that at least 6 men's snoring was associated to OSA? f) What is the probability that none of the women's snoring was associated to OSA?Explanation / Answer
Solution:-
a) The probability that atleast 3 men snore is 0.9975
x = 3, n = 18, p = 0.45
By applying binomial distribution:-
P(x, n) = nCxpx*(1-p)(n-x)
P(x > 3) = 0.9975
b) The probbaility that none of the men snore is 0.0000212.
x = 0, n = 18, p = 0.45
By applying binomial distribution:-
P(x, n) = nCxpx*(1-p)(n-x)
P(x = 0) = 0.0000212
c) The probabbility that fewer than 13 women snore is 0.9997.
x = 13, n = 18, p = 0.30
By applying binomial distribution:-
P(x, n) = nCxpx*(1-p)(n-x)
P(x < 13) = 0.9997
d) The probabbility that 7, 8, 9 or 10 women snore is 0.2722.
x = 7, 8, 9 or 10, n = 18, p = 0.30
By applying binomial distribution:-
P(x, n) = nCxpx*(1-p)(n-x)
P(x = 7, 8, 9 or 10) = P(x = 7) + P(x = 8) + P(x = 9) + P(x = 10)
P(x = 7, 8, 9 or 10) = 0.13762 + 0.081098 + 0.03862 + 0.0148955
P(x = 7, 8, 9 or 10) = 0.2722
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