BNAD 277 Ch. 6 prep questions

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Ch06 - Ch. 6 prep questions
Analytical Methods for Business (University of Arizona)

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ch06
Student:
1. A continuous random variable is characterized by uncountable values and can take on any value within an
interval.
True False

2. We are often interested in finding the probability that a continuous random variable assumes a
particular value.
True False

3. The probability density function of a continuous random variable can be regarded as a counterpart of the
probability mass function of a discrete random variable.
True False

4. Cumulative distribution functions can only be used to compute probabilities for continuous
random variables.
True False

5. The continuous uniform distribution describes a random variable, defined on the interval [a, b], that
has an equally likely chance of assuming values within any subinterval of [a, b] with the same length.
True False

6. The probability density function of a continuous uniform distribution is positive for all values between -
∞ and +∞.
True False

7. The mean of a continuous uniform distribution is simply the average of the upper and lower limits of the
interval on which the distribution is defined.
True False

8. The mean and standard deviation of the continuous uniform distribution are equal.
True False

9. The probability density function of a normal distribution is in general characterized by being symmetric
and bell-shaped.
True False

10. Examples of random variables that closely follow a normal distribution include the age and the class year
designation of a college student.
True False

11. Given that the probability distribution is normal, it is completely described by its mean μ > 0 and
its standard deviation σ > 0.
True False

12. Just as in the case of the continuous uniform distribution, the probability density function of the normal
distribution may be easily used to compute probabilities.
True False

13. The standard normal distribution is a normal distribution with a mean equal to zero and a standard
deviation equal to one.
True False
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14. The letter Z is used to denote a random variable with any normal
distribution. True False

15. The standard normal table is also referred to as the z
table. True False

16. Which of the following is correct?
A. A continuous random variable has a probability density function but not a cumulative distribution
function.
B. A discrete random variable has a probability mass function but not a cumulative distribution function.
C.A continuous random variable has a probability mass function, and a discrete random variable has a
probability density function.
D.A continuous random variable has a probability density function, and a discrete random variable has a
probability mass function.

17. Which of the following does not represent a continuous random variable?
A. Height of oak trees in a park.
B. Heights and weights of newborn babies.
C. Time of a flight between Chicago and New York.
D. The number of customer arrivals to a bank between 10 am and 11 am.

18. Which of the following is not a characteristic of a probability density function f(x)?
A. f(x) ≥ 0 for all values of x.
B. f(x) is symmetric around the mean.
C. The area under f(x) over all values of x equals one.
D. f(x) becomes zero or approaches zero if x increases to +infinity or decreases to -infinity.

19. The cumulative distribution function is denoted and defined as which of the following?
A. f(x) and f(x) = P(X ≤ x)
B. f(x) and f(x) = P(X ≥ x )
C. F(x) and F(x) = P(X ≤ x)
D. F(x) and F(x) = P(X ≥ x)

20. The cumulative distribution function F(x) of a continuous random variable X with the probability
density function f(x) is which of the following?
A. The area under f over all values x
B. The area under f over all values that are x or less
C. The area under f over all values that are x or more
D. The area under f over all non-negative values that are x or less

21. A continuous random variable has the uniform distribution on the interval [a, b] if its probability density
function f(x)
A. Is symmetric around its mean
B. Is bell-shaped between a and b
C. Is constant for all x between a and b, and 0 otherwise
D. Asymptotically approaches the x axis when x increases to +∞ or decreases to -∞

22. The height of the probability density function f(x) of the uniform distribution defined on the interval [a, b]
is
A. 1/(b - a) between a and b, and zero otherwise
B. (b - a)/2 between a and b, and zero otherwise
C. (a + b)/2 between a and b, and zero otherwise
D. 1/(a + b) between a and b, and zero otherwise