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# 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 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 meanμ = 82 and standard deviation σ = 20. 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)

) μ = 87 σ = 27 standardize x to z = (x - μ) / σ P(x &gt; 60) = P( z &gt; (60-87) / 27) = P(z &gt; -1) = 0.8413 (From... View the full answer

a) Z = 60 -82 /20 = -1.1  P(Z&gt;-1.1) = 0.8643 b)  Z = 110 -82 /20 = 1.4... View the full answer

a) P(X &gt; 60) = P(Z &gt; (60-82)/20) = P(Z &gt; -1.1) = 1- P(Z&lt;-1.1) = 1 - 0.1357 = 0.8643 b)... View the full answer

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