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 *μ* = 80
and standard deviation *σ* = 21. *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 125 (borderline diabetes starts at
125)

Answer #1

Solution :

Given that mean μ = 80 , standard deviation σ = 21

(a) x is more than 60

=> P(x > 60) = P((x - μ)/σ > (60 - 80)/21)

= P(Z > -0.9524)

= P(Z < 0.9524)

= 0.8289

(b) x is less than 110

=> P(x < 110) = P((x - μ)/σ < (110 - 80)/21)

= P(Z < 1.4286)

= 0.9236

(c) x is between 60 and 110

=> P(60 < x < 110) = P((60 - 80)/21 < (x - μ)/σ < (110 - 80)/21)

= P(-0.9524 < Z < 1.4286)

= 0.7525

(d) x is greater than 125

=> P(x > 125) = P((x - μ)/σ > (125 - 80)/21)

= P(Z > 2.1429)

= 1 − P(Z < 2.1429)

= 1 − 0.9838

= 0.0162

A person's blood glucose level and diabetes are closely related.
Let x be a random variable measured in milligrams of
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distribution that is approximately normal with mean ? = 82
and standard deviation ? = 20. Note: After 50
years of age, both the mean and standard deviation tend to
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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 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 = 21. Note: After 50
years of age, both the mean and standard deviation tend to
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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 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 = 82
and standard deviation σ = 23. Note: After 50
years of age, both the mean and standard deviation tend to
increase. For an adult (under 50) after a...

A person's blood glucose level and diabetes are closely related.
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glucose per deciliter (1/10 of a liter) of blood. Suppose that
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and standard deviation σ = 26. Note: After 50
years of age, both the mean and standard deviation tend to
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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 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 = 80 and standard deviation σ =
27. Note: After 50 years of age, both the mean and standard
deviation tend to increase. For an adult (under 50) after a...

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 = 89 and standard deviation σ =
23. Note: After 50 years of age, both the mean and standard
deviation tend to increase. For an adult (under 50) after a...

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 = 82 and standard deviation σ =
26. Note: After 50 years of age, both the mean and standard
deviation tend to increase. For an adult (under 50) after a...

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 = 89 and standard deviation σ =
29. Note: After 50 years of age, both the mean and standard
deviation tend to increase. For an adult (under 50) after a...

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 = 84 and standard deviation σ =
25. Note: After 50 years of age, both the mean and standard
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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 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 = 80 and standard deviation σ =
26. Note: After 50 years of age, both the mean and standard
deviation tend to increase. For an adult (under 50) after a...

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