Download CHAPTER 7 ASSIGNMENT

CHAPTER 7 ASSIGNMENT
CONTINUOUS PROBABILITY DISTRIBUTIONS
Name ___________________________________
______
Part I
Section __________
Score
Select the correct answer and write the appropriate letter in the space provided.
______ 1. In a uniform distribution
a. the mean and the median are always equal.
b. the mean and the standard deviation are always equal.
c. the mean is always larger than the median.
d. the mean is always smaller than the median.
2. A uniform probability distribution
a. has a total area equal to 1.0.
b. is completely determined by its minimum and maximum values.
c. can be represented graphically by a rectangle with length = (b-a) and height = 1/(ba).
d. all of the above.
______ 3. The normal probability distribution is
a. a bell-shaped distribution.
c. symmetric.
b.
d.
a continuous distribution.
all of the above.
______ 4. The standard normal probability distribution
a. is a special case of the normal probability distribution.
b. has a mean equal to 0 and a standard deviation equal to 1.
c. measures the distance from the mean in units of the standard deviation.
d. all of the above.
______ 5. A normal probability distribution is completely described by
a. its mean.
b. its standard deviation.
c. its mean and standard deviation.
d. none of the above.
______ 6. A normal probability distribution
a. can be converted to a standard normal distribution using the formula z 
xμ
.
σ
b. is asymmetric
c. can not have a z-score greater than 3 or less than -3.
d. always has a mean value that is greater than zero.
______ 7. A normal probability distribution
a. has at least two peaks.
c. increases as X increases.
Chapter 7
b.
d.
is asymptotic.
is discrete.
Continuous Probability Distributions
The Normal Probability Distribution
______ 8. The uniform probability distribution
a. has a standard deviation equal to
 b  a 

.
b. has a mean equal to its variance.
c. conforms to the Empirical Rule
d. is symmetric.
______ 9. What percent of the area under the normal curve is within   1 ?
a. 68%.
b. 34%.
c. 95%.
d. none of the above.
______ 10. A z value
a. is the standard deviation for the standard normal probability distribution.
b. is a measure of how many standard deviations the mean is from the median.
c. is the difference of the mean and the probability of z.
d. is a measure of how many standard deviations a particular score is from the mean.
Part II
11.
Answer the following questions. Be sure to show your work.
A statistics instructor collected data on the time it takes the students to complete a test. The
test taking time is uniformly distributed within a range of 35 minutes to 55 minutes.
a. Determine the height and draw this uniform distribution.
b. How long does the average test take?
b.
c. Determine the standard deviation of the test taking time.
c.
Chapter 7
Continuous Probability Distributions
The Normal Probability Distribution
d.
What is the probability a particular student will take less than 45 minutes?
d.
e. What is the probability a particular student will take between 45 and 50 minutes?
e.
12.
Suppose that gas mileage for a 2006 Eco is a uniformly distributed random variable between 40
and 44 miles per gallon.
a. What is the probability that the gas mileage exceeds 43 miles per gallon?
a.
b. What is the probability that gas mileage will be between 41 and 43 miles per gallon?
b.
c. What is the expected gas mileage for the Ecko ?
c.
Chapter 7
Continuous Probability Distributions
The Normal Probability Distribution
13. Fix-It Copiers advertises a mean time of 100 minutes for office calls with a standard deviation
of 25 minutes. Assuming that the repair time is normally distributed, what percentage of calls
are completed:
a. between 100 and 120 minutes?
a.
b. in less than 120 minutes?
b.
c. in less than 60 minutes?
c.
d. between 120 and 150 minutes?
d.
e. between 60 and 120 minutes?
e.
f.
Twenty percent of their jobs take more than how much time?
f.
Chapter 7
Continuous Probability Distributions
The Normal Probability Distribution
14.
A certain printer cartridge has demonstrated a mean usage time of 9 hours and a standard
deviation of 22 minutes. Assuming that usage time is a normal random variable, what usage
time guarantee (in hours) should the manufacturer advertise in order to ensure that only 4% of
the cartridges fail to meet the guaranteed usage time?
13.
Chapter 7
Continuous Probability Distributions
The Normal Probability Distribution