In: Statistics and Probability

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 = 88 and estimated standard deviation σ = 28. 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 approximately normal with μx = 88 and σx = 19.80. The probability distribution of x is approximately normal with μx = 88 and σx = 14.00. The probability distribution of x is approximately normal with μx = 88 and σx = 28. The probability distribution of x is not normal. 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

(f) Explain what this might imply if you were a doctor or a nurse. The more tests a patient completes, the weaker is the evidence for lack of insulin. The more tests a patient completes, the stronger is the evidence for lack of insulin. The more tests a patient completes, the weaker is the evidence for excess insulin. The more tests a patient completes, the stronger is the evidence for excess insulin.

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 = 96 and estimated standard deviation σ = 47. 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 = 84 and estimated standard deviation σ = 29. 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 = 60and 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 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 = 86 and estimated standard deviation σ = 35. A
test result x < 40 is an indication of severe excess
insulin, and medication is usually prescribed.
(d) Repeat part (b) for n = 5 tests...

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 = 71 and estimated standard deviation σ = 30. 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 = 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 = 51 and
estimated standard deviation σ = 47. 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 = 24. 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 = 51 and
estimated standard deviation σ = 47. 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 = 52 and estimated standard deviation σ = 10. 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...

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