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 = 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 test, x < 40? (Round your answer to three 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? The probability distribution of x is approximately normal with μx = 51 and σx = 23.50. The probability distribution of x is approximately normal with μx = 51 and σx = 47. The probability distribution of x is approximately normal with μx = 51 and σx = 33.23. The probability distribution of x is not normal. What is the probability that x < 40? (Round your answer to three decimal places.) (c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to three decimal places.) (d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to three 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 weaker is the evidence for excess insulin. 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 stronger is the evidence for excess insulin.

Solution :

Given that ,

mean = = 51

standard deviation = = 47

a) P(x < 40) = P[(x - ) / < (40 - 51) / 47]

= P(z < -0.23)

Using z table,

= 0.4090

b) n = 2

= = 51

= / n = 47/ 2 = 33.23

The probability distribution of x is approximately normal with μx = 51 and σx = 33.23

P( < 40) = P(( - ) / < (40 - 51) / 33.23)

= P(z < -0.33)

Using z table

= 0.3707

c) n = 3

= = 51

= / n = 47/ 3 = 27.14

The probability distribution of x is approximately normal with μx = 51 and σx = 27.14

P( < 40) = P(( - ) / < (40 - 51) / 27.14)

= P(z < -0.41)

Using z table

= 0.3409

d) n = 5

= = 51

= / n = 47/ 5 = 21.02

The probability distribution of x is approximately normal with μx = 51 and σx = 21.02

P( < 40) = P(( - ) / < (40 - 51) / 21.02)

= P(z < -0.52)

Using z table

= 0.3015

e) yes,

The more tests a patient completes, the weaker 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 = 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,...

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 = 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...

ADVERTISEMENT

ADVERTISEMENT

Latest Questions

- A 12 in. x 18 in. rectangular beam has an effective span of 20 ft. A...
- Standard Costs, Decomposition of Budget Variances, Direct Materials and Direct Labor Haversham Corporation produces dress shirts....
- Suppose you held a diversified portfolio consisting of a $7,500 investment in each of 20 different...
- please answer all Crane Limited purchased a machine on account on April 2, 2018, at an...
- Problem 1. Molecular Genetics A sea urchin mutation results in an unusual positioning of the mitotic...
- Explain, in your own words, what Thomson means when she claims that “Being a good K...
- This class should include .cpp file, .h file and driver.cpp (using the language c++)! Overview of...

ADVERTISEMENT