Question

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* = 6950 and estimated standard deviation *σ*
= 2950. 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.)

(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 not normal.

The probability distribution of *x* is approximately
normal with *μ*_{x} = 6950 and
*σ*_{x} = 1475.00.

The probability distribution of *x* is
approximately normal with *μ*_{x} = 6950
and *σ*_{x} = 2950.

The probability distribution of *x* is approximately
normal with *μ*_{x} = 6950 and
*σ*_{x} = 2085.97.

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.)

(d) Compare your answers to parts (a), (b), and (c). How did the
probabilities change as *n* increased?

The probabilities decreased as *n* increased.

The probabilities increased as *n*
increased.

The probabilities stayed the same as *n* increased.

(e) If a person had *x* < 3500 based on three tests, what
conclusion would you draw as a doctor or a nurse?

It would be an extremely rare event for a person to have two or three tests below 3,500 purely by chance. The person probably has leukopenia.

It would be an extremely rare event for a person to have two or three tests below 3,500 purely by chance. The person probably does not have leukopenia.

It would be a common event for a person to have two or three tests below 3,500 purely by chance. The person probably has leukopenia.

It would be a common event for a person to have two or three tests below 3,500 purely by chance. The person probably does not have leukopenia.

(f) It is known that 85% of all new products introduced in grocery stores fail (are taken off the market) within 2 years. If a grocery store chain introduces 65 new products, find the following probabilities. (Round your answers to four decimal places.)

within 2 years 47 or more fail

within 2 years 58 or fewer fail

within 2 years 15 or more succeed

within 2 years fewer than 10 succeed

Answer #1

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...

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 = 6900 and estimated standard deviation σ
= 2100. 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 = 6150 and estimated standard deviation σ
= 2300. 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 = 6600 and
estimated standard deviation σ = 2450. 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 = 8250 and estimated standard deviation σ
= 2900. 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 = 6700 and
estimated standard deviation σ = 2700. 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 ? = 6600 and estimated standard deviation ?
= 2350. 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 ? = 7950 and estimated standard deviation ?
= 2600. 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 = 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 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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