If f (x) is the probability density function for the blood cholesterol level of men over the age of 40, where x is measured in milligrams per deciliter, express as an integral the probability that the cholesterol level of such a man lies between 185 and

1
If f (x) is the probability density function for
the blood cholesterol level of men over the age
of 40, where x is measured in milligrams per
deciliter, express as an integral the probability
that the cholesterol level of such a man lies
between 185 and 240.

1. image
2. image
3. image
4. image

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2
Let the function whose graph is shown be a
probability density function. Calculate the mean.
applet

1. 3.5
2. 6
3. 5
4. 5.5
5. 2.5
6. 3

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3
A type of lightbulb is labeled as having an
average lifetime of 2,000 hours. It's reasonable
to model the probability of failure of these
bulbs by an exponential density function with
mean image . What is the median lifetime of
these lightbulbs?

1. 970.41 hours
2. 1,247.66 hours
3. 1,802.18 hours
4. 1,524.92 hours
5. 1,386.29 hours
6. 2,079.44 hours

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4
According to the National Health Survey, the
heights of adult males in the United States are
(normally distributed with mean) 72 inches, and
standard deviation of 2.8 inches. What is the
probability that an adult male chosen at random
is between 70 inches and 75 inches tall?

1. 0.81
2. 0.68
3. 0.43
4. 0.31
5. 0.56
6. 0.62

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5
The standard deviation for a random variable with
probability density function f and mean image
is defined by image Find the standard deviation
for an exponential density function with mean 20.

1. 16
2. 26
3. 12
4. 28
5. 20
6. 24

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6
The hydrogen atom is composed of one proton in
the nucleus and one electron, which moves about
the nucleus. In the quantum theory of atomic
structure, it is assumed that the electron does
not move in a well-defined orbit. Instead, it
occupies a state known as an orbital, which may
be thought of as a quotcloudquot of negative
charge surrounding the nucleus. At the state of
lowest energy, called the ground state, or
1s-orbital, the shape of this cloud is assumed to
be a sphere centered at the nucleus. This sphere
is described in terms of the probability density
function image where image is the Bohr radius
( image ). The integral image gives the
probability that the electron will be found
within the sphere of radius r meters centered at
the nucleus. Find the probability that the
electron will be within the sphere of radius
image centered at the nucleus.

1. 0.17
2. 0.54
3. 0.86
4. 0.2
5. 0.44
6. 0.48

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