Question

Let *x* be a random variable that represents the level of
glucose in the blood (milligrams per deciliter of blood) after a
12-hour fast. Assume that for people under 50 years old, *x*
has a distribution that is approximately normal, with mean
*μ* = 92 and estimated standard deviation *σ* = 40. A
test result *x* < 40 is an indication of severe excess
insulin, and medication is usually prescribed.

(a) What is the probability that, on a single test, *x*
< 40? (Round your answer to four decimal places.)

(b) Suppose a doctor uses the average *x* for two tests
taken about a week apart. What can we say about the probability
distribution of *x*? *Hint*: See Theorem 7.1.

The probability distribution of *x* is not normal.

The probability distribution of *x* is approximately
normal with *μ*_{x} = 92 and
*σ*_{x} = 40.

The probability distribution of *x* is approximately normal
with *μ*_{x} = 92 and
*σ*_{x} = 28.28.

The probability distribution of *x* is approximately
normal with *μ*_{x} = 92 and
*σ*_{x} = 20.00.

What is the probability that *x* < 40? (Round your answer
to four decimal places.)

(c) Repeat part (b) for *n* = 3 tests taken a week apart.
(Round your answer to four decimal places.)

(d) Repeat part (b) for *n* = 5 tests taken a week apart.
(Round your answer to four decimal places.)

(e) Compare your answers to parts (a), (b), (c), and (d). Did the
probabilities decrease as *n* increased?

Yes

No

Explain what this might imply if you were a doctor or a nurse.

The more tests a patient completes, the stronger is the evidence for lack of insulin.

The more tests a patient completes, the stronger is the evidence for excess insulin.

The more tests a patient completes, the weaker is the evidence for excess insulin.

The more tests a patient completes, the weaker is the evidence for lack of insulin.

Answer #1

Let x be a random variable that represents the level of glucose
in the blood (milligrams per deciliter of blood) after a 12 hour
fast. Assume that for people under 50 years old, x has a
distribution that is approximately normal, with mean μ = 60 and
estimated standard deviation σ = 44. A test result x < 40 is an
indication of severe excess insulin, and medication is usually
prescribed. (a) What is the probability that, on a single...

Let x be a random variable that represents the level of glucose
in the blood (milligrams per deciliter of blood) after a 12 hour
fast. Assume that for people under 50 years old, x has a
distribution that is approximately normal, with mean μ = 79 and
estimated standard deviation σ = 32. A test result x < 40 is an
indication of severe excess insulin, and medication is usually
prescribed. (a) What is the probability that, on a single...

Let x be a random variable that represents the level of
glucose in the blood (milligrams per deciliter of blood) after a 12
hour fast. Assume that for people under 50 years old, x
has a distribution that is approximately normal, with mean
μ = 56 and estimated standard deviation σ = 42. A
test result x < 40 is an indication of severe excess
insulin, and medication is usually prescribed.
(a) What is the probability that, on a single...

Let x be a random variable that represents the level of glucose
in the blood (milligrams per deciliter of blood) after a 12 hour
fast. Assume that for people under 50 years old, x has a
distribution that is approximately normal, with mean μ = 62 and
estimated standard deviation σ = 31. A test result x < 40 is an
indication of severe excess insulin, and medication is usually
prescribed.
(a) What is the probability that, on a single...

Let x be a random variable that represents the level of
glucose in the blood (milligrams per deciliter of blood) after a 12
hour fast. Assume that for people under 50 years old, x has a
distribution that is approximately normal, with mean μ = 60 and
estimated standard deviation σ = 46. A test result x < 40 is an
indication of severe excess insulin, and medication is usually
prescribed.
(a) What is the probability that, on a single...

Let x be a random variable that represents the level of
glucose in the blood (milligrams per deciliter of blood) after a 12
hour fast. Assume that for people under 50 years old, x
has a distribution that is approximately normal, with mean
μ = 90and estimated standard deviation σ = 49. A
test result x < 40 is an indication of severe excess
insulin, and medication is usually prescribed.
(a) What is the probability that, on a single test,...

Let x be a random variable that represents the level of
glucose in the blood (milligrams per deciliter of blood) after a
12-hour fast. Assume that for people under 50 years old, x
has a distribution that is approximately normal, with mean
μ = 78 and estimated standard deviation σ = 45. A
test result x < 40 is an indication of severe excess
insulin, and medication is usually prescribed.
(a) What is the probability that, on a single test,...

Let x be a random variable that represents the level of glucose
in the blood (milligrams per deciliter of blood) after a 12 hour
fast. Assume that for people under 50 years old, x has a
distribution that is approximately normal, with mean μ = 94 and
estimated standard deviation σ = 40. A test result x < 40 is an
indication of severe excess insulin, and medication is usually
prescribed.
(a) What is the probability that, on a single...

Let x be a random variable that represents the level of
glucose in the blood (milligrams per deciliter of blood) after a 12
hour fast. Assume that for people under 50 years old, x
has a distribution that is approximately normal, with mean
? = 59 and estimated standard deviation ? = 45. A
test result x < 40 is an indication of severe excess
insulin, and medication is usually prescribed.
(a) What is the probability that, on a single...

Let x be a random variable that represents the level of
glucose in the blood (milligrams per deciliter of blood) after a
12-hour fast. Assume that for people under 50 years old, x
has a distribution that is approximately normal, with mean
μ = 57 and estimated standard deviation σ = 34. A
test result x < 40 is an indication of severe excess
insulin, and medication is usually prescribed.
(a) What is the probability that, on a single test,...

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