Stewart_Calc_7ET ch08sec05
MULTIPLE CHOICE
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 195 and .
a.
b.
c.
d.
e.
2. A spinner from a board game randomly indicates a real number between 0 and . The
spinner is fair in the sense that it indicates a number in a given interval with the same
probability as it indicates a number in any other interval of the same length. Find the mean.
a.
4
b.
3
c.
7
d.
5
e.
8
f.
3. According to the National Health Survey, the heights of adult males in the United States are
(normally distributed with mean) 73 inches, and standard deviation of 2.8 inches. What is the
probability that an adult male chosen at random is between inches and inches tall?
a.
b.
0.7154
c.
0.2812
d.
0.6512
e.
0.5222
f.
0.5528
4. The standard deviation for a random variable with probability density function f and mean µ is
defined
.
Find the standard deviation for an exponential density function with mean .
a.
b.
c.
d.
e.
5. Suppose the average waiting time for a customer’s call to be answered by a company
representative (modeled by exponentially decreasing probability density functions) is
minutes. Find the median waiting time.
a.
minutes
b.
minutes
c.
minutes
d.
minutes
e.
minutes
6. The manager of a fast-food restaurant determines that the average time that her customers wait
for service is 2 minutes. Find the probability that a customer is served within the first
minutes.
a.
b.
c.
d.
e.
NUMERIC RESPONSE
1. For any normal distribution, find to two decimal places.
2. Boxes are labeled as containing 500 g of cereal. The machine filling the boxes produces
weights that are normally distributed with standard deviation 12 g. If the target weight is 500
g, what is the probability that the machine produces a box with less than g of cereal?
Round your answer to four decimal places.
3. The manager of a fast-food restaurant determines that the average time that her customers wait
for service is 2 minutes.
The manager wants to advertise that anybody who isn’t served within a certain number of
minutes gets a free hamburger. But she doesn’t want to give away free hamburgers to more
than % of her customers. What value of x must she use in the advertisement “if you aren’t
served within x minutes, you get a free hamburger”?
4. A type of lightbulb is labeled as having an average lifetime of hours. It’s reasonable to
model the probability of failure of these bulbs by an exponential density function with mean µ
= . What is the median lifetime of these lightbulbs? Give your answer rounded to two
decimal places.
5. Let the function whose graph is shown be a probability density function. Calculate the mean.
6. Let
a) For what value of c is f a probability density function?
b) For that value of c, find P (–1 < X < 1).