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
*?* = 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 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 not normal.The
probability distribution of *x* is approximately normal with
*?*_{x} = 59 and
*?*_{x} = 45. The
probability distribution of *x* is approximately normal with
*?*_{x} = 59 and
*?*_{x} = 22.50.The probability
distribution of *x* is approximately normal with
*?*_{x} = 59 and
*?*_{x} = 31.82.

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?

YesNo

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

a)

P(X<40)=P(Z<(40-59)/45)=P(Z<-0.42)=0.3372 ( please try 0.3364 if this comes wrong)

b).The probability distribution of x is approximately normal with x = 59 and x = 31.82.

P(Xbar<40)=P(Z<(40-59)/(45/sqrt(2))=P(Z<-0.60)=0.2743 (please try 0.2752 if this comes wrong)

c)

P(Xbar<40)=P(Z<(40-59)/(45/sqrt(3))=P(Z<-0.73)=0.2327 (please try 0.2323 if this comes wrong)

d)

P(Xbar<40)=P(Z<(40-59)/(45/sqrt(5))=P(Z<-0.94)=0.1736 (please try 0.1726 if this comes wrong)

e)

yes

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 = 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...

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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
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Let x be a random variable that represents the level of
glucose in the blood (milligrams per deciliter of blood) after a 12
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