Question 422965: A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean μ = 83 and standard deviation σ = 22. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.)
(a) x is more than 60
(b) x is less than 110
(c) x is between 60 and 110
(d) x is greater than 140 (borderline diabetes starts at 140)
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A person's blood glucose level and diabetes are closely related.
Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood.
Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean μ = 83 and standard deviation σ = 22. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.)
(a) x is more than 60
z(60) = (60-83)/22 = -1.0455
P(x > 60) = P(z > -1.0455) = 0.8521
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(b) x is less than 110
z(110) = (110-83)/22 = 1.2273
P(x < 110) = P(z < 1.2273) = 0.8901
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(c) x is between 60 and 110
Find the 2 z-values; then find the area between them.
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(d) x is greater than 140 (borderline diabetes starts at 140)
Find the z-value; then find its right tail.
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Cheers,
Stan H.
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