I.
MULTIPLE CHOICE
The following statements are vital in strengthening your
discernment on aspects of decision making through the process of PROBABILITY AND STATISTICS. Write TRUE
if the statement suffices affirmation that substantiates the claims while FALSE
if the statement nullifies the assertions. (2 points each)
1. The
measure of voltage for a smoke detector battery can be any value between 0
volts and 9 volts. It is therefore a discrete random variable.
2. A
probability distribution gives the probability for each value of the random
variable.
3. The
count of the number of patrons viewing a movie is finite number and is
therefore a continuous random variable.
4. The
requirements for a discrete probability distribution are 0 ≤ p(x) ≤ 1
and 
≤ 1.
≤ 1.
5. Toss
two fair coins and let x
equal the number of heads observed. HH
appears one in eight.
6. The
Poisson distribution provides a simple, easy-to-compute, and accurate
information to binomial probabilities when n is
large and np is
small.
7. A
binomial experiment consists of n
identical trials with probability of success p
on each trial.
8. The
probability density function f(x),
defined over the set of real numbers, has a total probability value which is
greater than one.
9. The
cumulative distribution F(x) of
a continuous random variable X with
density function f(x)
has P(X ≤ x).
10. The
joint probability distribution is a situation when probability distribution of
random variables’ simultaneous occurrence can be represented by f(x, y) for any pair
of values (x, y).
11. The
f(x, y) is
a joint density function of the continuous random variables X and Y if it has
probability equal to one f(x,
y) ≤ 0.
12. The
population mean is the value that you would expect to observe if the experiment
is repeated over and over again.
13. The
normal approximation is appropriate for binomial random variable.
14. The
probability distribution can either be discrete or continuous.
15. There
must be only two possible outcomes for Poisson probability distribution.
II.
PROBLEM SOLVING
The decision making process can be
applied in a variety of everyday situations and across most academic
disciplines. In the following applications, you are going to execute what you
relatively understood from the fundamental analysis.
1.
Over a long period of time, it has
been observed that a professional basketball player can make on a given trial
with probability equal to 0.80. Suppose he shoots four free throws, what is the
probability that he will make at least one free throw? (5 points)
2.
The average number of traffic
accidents on a certain section of highway is two per week. Determine the
probability of at most three accidents on this section of highway during a
two-week period. (5 points)
3.
QGC
bids on a job to construct a building. If the bid is won, there is a 0.70
probability of making a Php 7,500,000.00 profit and there is a probability of
0.30 that the contractor will break even. What is the expected value? Should
the bid be submitted? (10 points)
4.
For
what value of k, f(x,
y) represents the
probability density function of two continuous random variables X and Y, where
f(x,
y) =
(10 points)
(10 points)
5.
A
random variable X has the following probability function.
Find P(x ≤ 4).
X
|
0
|
1
|
2
|
3
|
4
|
5
|
6
|
7
|
P(X)
|
0
|
k
|
2k
|
2k
|
3k
|
k2
|
2k2
|
7k2 + k
|
(10
points)
6.
Suppose
that you must establish regulations concerning the maximum number of people who
can occupy the elevator. A study of elevator occupancies indicates that if
eight people occupy the elevator, the probability distribution of the total
weight of the eight people has a mean equal to 1200 pounds and a standard
deviation of 99 pounds. What is the probability that the total weight of eight
people exceeds 1300 pounds? 1500 pounds? Assume that the distribution is
approximately normal. (10 points)
7.
The
reliability of the strength of concrete is the probability that a concrete
specimen, chosen at random from production will function under its designed
conditions. Random samples of 100 concrete specimens were tested. With the
compressive strength reliability of 0.98, calculate the mean and standard
deviation of the under conditioned strength of the specimens. (10 points)
8.
On the
exam for Civil Engineers, scores are normally distributed with a mean of 615
and a standard deviation of 107. If an institution requires scores above the 70TH
percentile for entering Master of Science in Structural Engineering, determine
the cut-off point. (10 points)
0 comments:
Post a Comment