Question

6.5 - 9 and 10)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 = 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.)

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(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 = 84 and σx = 42.

The probability distribution of x is approximately normal with μx = 84 and σx = 21.00.

The probability distribution of x is not normal.

The probability distribution of x is approximately normal with μx = 84 and σx = 29.70.

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.)____________

Question 10 ) 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 = 6800 and estimated standard deviation σ = 2850. 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 3500? (Round your answer to four decimal places.)
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(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 μ_x = 6800 and σ_x = 2850.The probability distribution of x is approximately normal with μ_x = 6800 and σ_x = 2015.25.    The probability distribution of x is approximately normal with μ_x = 6800 and σ_x = 1425.00.The probability distribution of x is not normal.

What is the probability of x < 3500? (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.)_____________

Answer 1

Solution :

9) Given that ,

mean = = 84

standard deviation = = 42

a) P(x < 40) = P[(x - ) / < (40 - 84) / 42]

= P(z < -1.05)

Using z table,

= 0.1469

b) n = 2

= = 84

= / n = 42/ 2 = 29.70

The probability distribution of x is approximately normal with μx = 84 and σx = 29.70

P( < 40) = P(( - ) / < (40 - 84) / 29.70)

= P(z < -1.48)

Using z table

= 0.0694

c) n = 3

= = 84

= / n = 42/ 3 = 24.25

The probability distribution of x is approximately normal with μx = 84 and σx = 24.25

P( < 40) = P(( - ) / < (40 - 84) / 24.25)

= P(z < -1.81)

Using z table

= 0.0351

d) n = 5

= = 84

= / n = 42/ 5 = 18.78

The probability distribution of x is approximately normal with μx = 84 and σx = 18.78

P( < 40) = P(( - ) / < (40 - 84) / 18.78)

= P(z < -2.34)

Using z table

= 0.0096

10) Given that ,

mean = = 6800

standard deviation = = 2850

a) P(x < 3500) = P[(x - ) / < (3500 - 6800) / 2850]

= P(z < -1.16)

Using z table,

= 0.1230

b) n = 2

= = 6800

= / n = 2850/ 2 = 2015.25

The probability distribution of x is approximately normal with μx = 6800 and σx = 2015.25

P( < 3500) = P(( - ) / < (3500 - 6800) / 2015.25)

= P(z < -1.64)

Using z table

= 0.0505

c) n = 3

= = 6800

= / n = 2850/ 3 = 1645.45

The probability distribution of x is approximately normal with μx = 6800 and σx = 1645.45

P( < 3500) = P(( - ) / < (3500 - 6800) / 1645.45)

= P(z < -2.01)

Using z table

= 0.0222