A person\'s blood glucose level and diabetes are closely related. Let x be a ran

Question

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 8 and standard deviatio 20. ote: After 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 greaer than 140 (borderline diabetes starts at 140)

Explanation / Answer

We are allowed to do 1 question at a time. Post again for second question.

a) x is more than 60
z(60) = (60-80)/20 = -1.00
P(x > 60) = P(z > -1.00) = 0.84134
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(b) x is less than 110
z(110) = (110-80)/20 = 1.5

P(x < 110) = P(z < 1.5) = 0.9332
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(c) x is between 60 and 110

P(60 < x < 110) = P(- 1.0 < z < 1.5) = P(z < 1.5) - P( z > -1.0) = 0.7745

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(d) x is greater than 140 (borderline diabetes starts at 140)
Find the z-value; then find its right tail.

z(40) = (140-80)/20 = 3

P(x > 140) = P(z > 3) = 0.00135

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