7. After going through this lesson, you
are able to:
1. define a normal random variable;
2. illustrate a normal random
variable and its characteristics;
8. After going through this lesson, you
are able to:
3. listen attentively during class
discussion;
4. participate actively in activities;
and
9. After going through this lesson, you
are able to:
5. appreciate the importance of the
lesson being discussed.
16. Mean is equal to the
summation of scores
divided by the
number of cases.
17.
18. The distribution of the
height (X) in centimeter
(cm) of the 16 teachers of
Naic Integrated NHS-
SHS was presented on the
table. Construct a
histogram for the random
variable (X).
27. Normal Probability
Distribution
• It is used to describe the
characteristics of populations and
help us visualize the inferences we
make about the population.
28. Normal Probability
Distribution
• It also used to determine the
probabilities and percentile of
the continuous random
variables in the distribution.
29. Properties of Normal Curve
1. The normal curve is bell-
shaped.
2. The curve is
symmetrical about its
center.
30. Properties of Normal Curve
3. The mean, median, and mode
coincide at the center.
4. The width of the curve is
determined by the standard
deviation of the distribution.
31. Properties of Normal Curve
5. The tails of the curve are plotted
in both directions and flatten out
indefinitely along the horizontal axis.
The tails are thus asymptotic to the
baseline
6. The total area under a normal
curve is 1
33. A normally distributed random variable with a mean μ =
0 and standard deviation ơ = 1 is called a standard
normal variable
34. The shape of a normal curve is based on the
two given parameters, the mean and the
standard deviation of the distribution.
When comparing two distributions each
described by the normal curve, the following
are the three situations based on the said
parameters
35. When the means are not equal, but the standard
deviations are equal. (μ1 ≠ μ2 ; ơ1 =ơ2 ), the
curves have a similar shape but centered at
different points
36. When the means are equal, but the standard deviations
are not equal. (μ1 = μ2 ; ơ1 ≠ ơ2 ), the curves are
centered at the same point but they have different
height and spreads
37. When the means are different and the standard
deviations are also different (μ1≠ μ2 ; ơ1 ≠ ơ2 ), the
curves are centered at different points and vary in
shapes
38. Analyze the following figures and
describe each by identifying
whether they have the same or
different mean and standard
deviation.
40. After going through this lesson, you
are able to:
1. Calculate the mean and the
variance of a discrete random
variable;
41. Recall the formula for:
1.Expected Value or Mean Value
2.Variance
3.Standard Deviation
42. The table below shows the probability
distribution of the number of girls in a family
of three children in Barangay Maligaya.
Calculate the mean and variance of the random
variable with the given probability distribution.
45. Questions:
1. If you are Cardo, would you buy a raffle ticket?
Why?
2. If Cardo decided to buy five tickets, what is the
probability that he would win the prize if 1000 tickets
were sold?
What is the probability that Cardo will lose the bet?
3. How much money will Cardo gain if he wins the
prize?
46. Questions:
4. How much money will be wasted if he will not
win the prize and he buy one ticket?
5. What if 1000 tickets were purchased by
different individuals, what is the expected value
of buying one ticket?
6. How would you describe Romulo as a friend?
52. The negative value (in expected value)
means that one loses money on the
average.
Having this knowledge, you can now
make a wise decision.
53. But remember, important things should be
prioritized. If you can afford to buy tickets
without sacrificing your essential needs. It is
okay to take a chance sometimes. You should also
consider saving money for future use, because
not every day you have enough funds, having
extra money would be a great help in times of
need.
