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* = 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 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 *μ*_{x} = 56 and
*σ*_{x} = 21.00.The probability
distribution of *x* is not
normal. The probability distribution
of *x* is approximately normal with
*μ*_{x} = 56 and
*σ*_{x} = 29.70.The probability
distribution of *x* is approximately normal with
*μ*_{x} = 56 and
*σ*_{x} = 42.

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. T

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

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

Answer #1

Solution:-

(a) Given that μ = 56 , σ = 42

P(X < 40) = P((X-μ)/σ < (40-56)/42)

= P(Z < -0.3810)

= 0.3520

(b) Given that μx = 56, σx = 21.00

P(X < 40) = P(Z < (40-56)/21)

= P(Z < -0.7619)

= 0.2236

(c) For n = 3, σx = 24.25

P(X < 40) = P(Z < 40-56)/24.25)

= P(Z < -0.6598)

= 0.2546

(d) For n = 5, σx = 18.78

P(X < 40) = P(Z < 40-56)/18.78)

= P(Z < -0.8520)

= 0.1977

(e) yes.

=>option B.The more tests a patient completes,the stronger is the evidence for excess insulin

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