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 = 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 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 6.1. The probability distribution of x is approximately normal with μx = 79 and σx = 22.63. The probability distribution of x is not normal. The probability distribution of x is approximately normal with μx = 79 and σx = 16.00. The probability distribution of x is approximately normal with μx = 79 and σx = 32. 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 weaker is the evidence for excess 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 lack of insulin. The more tests a patient completes, the stronger is the evidence for lack of insulin. Need Help? Read It Watch It

Answer #1

Given Normal distribution N(79,32)

mean μ = 79 and estimated standard deviation σ = 32

a) the probability that, on a single test, x < 40

P(X<40)

for x =40, Z = (40 - 79)/32 = -1.21875

P(X<40) = P(Z<-1.21875) = 0.1115

b) The sample follows approximately normal distribution N(μ , )

The probability distribution of x is approximately normal with μx = 79 and σx = 22.63.

the probability that x < 40

= -1.7236

P(X<40) = P(Z<-1.7236) = 0.0424

c) for n = 3

Z = -2.1109

P(X<40) = P(Z<-2.1109) = 0.0174

d) for n = 5

Z = -2.7252

P(X<40) = P(Z<-2.7252) =0.0032

e) as the n increases the probability decreases, 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 = 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 = 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 = 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,...

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
? = 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,...

Let x be a random variable that represents white blood
cell count per cubic milliliter of whole blood. Assume that
x has a distribution that is approximately normal, with
mean μ = 6000 and estimated standard deviation σ
= 2150. A test result of x < 3500 is an indication of
leukopenia. This indicates bone marrow depression that may be the
result of a viral infection.
(a) What is the probability that, on a single test, x
is less than...

Let x be a random variable that represents white blood cell
count per cubic milliliter of whole blood. Assume that x has a
distribution that is approximately normal, with mean μ = 6400 and
estimated standard deviation σ = 2050. A test result of x < 3500
is an indication of leukopenia. This indicates bone marrow
depression that may be the result of a viral infection. (a) What is
the probability that, on a single test, x is less than...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 2 minutes ago

asked 7 minutes ago

asked 8 minutes ago

asked 9 minutes ago

asked 18 minutes ago

asked 19 minutes ago

asked 23 minutes ago

asked 25 minutes ago

asked 28 minutes ago

asked 28 minutes ago

asked 37 minutes ago

asked 37 minutes ago