The document covers Chapter 8 on probability distribution, detailing discrete and continuous random variables, including binomial and normal distributions. It provides examples for calculating probabilities, means, variances, and standard deviations related to binomial and normal distributions. Additionally, it includes homework assignments for further practice.

1. CHAPTER 8:
PROBABILITY
DISTRIBUTION
PREPARED BY : UMMU ‘ATHIRAH BINTI MOHD NAWAWI
PREPARED FOR : MATHEMATICS DEPARTMENT
DAY / DATE : SATURDAY (30/05/15)

2. PROBABILITY DISTRIBUTION
DISCRETE RANDOM VARIABLE
1) Finite and Countable
2) eg: gender, toss a
coin, toss a dice
Binomial
Distribution
CONTINUOUS RANDOM
VARIABLES
1) Indefinite and uncountable
rv in certain range
2) eg: mass of 5B members,
height, etc
Normal
Distribution

3. 8.1 BINOMIAL DISTRIBUTION
•Bernoulli trial – trial with only two outcomes, success
or failure
•Bernoulli trial repeated many times – Binomial
experiment
•X = Discrete rv
•n = number of experiment
•p = probability of success

4. •Probability of obtaining r successes in binomial distribution
P = probability
X= Bin rv
r = no of success
n = no of trial
p = probability of success ( 0<p<1)
q = probability of failure (q = 1 – p)
r
n
r
r
n
q
p
C
r
X
P 

 )
(

5. EXAMPLES
1) Ronaldo has taken 3 shots in an archery practice. The
probability that Ronaldo strikes the target is 0.6. X
represent the number of times Ronaldo strikes the target.
a) List the elements of binomial distn rv
b) Find the probability that Ronaldo strikes the target
i) exactly three times
ii) at least one times

6. SOLUTION
a) i) P(X=3)
= 0.216
ii) P(X
= 1 -
= 1 -
= 1-
= 1 – 0.064
= 0.936
3
3
3
3
3
)
6
.
0
1
(
)
6
.
0
( 

C
0
3
0
0
3
)
6
.
0
1
(
)
6
.
0
( 

C

7. 2) 40% of the application for the MARA scholarship are not
accepted. In a school, 7 students apply for the MARA
scholarships. Calculate the probability that
a)Exactly three applications are not accepted.
b)At least two applications are not accepted.
Solution:
X – number of applications that are not accepted.
X B(7, 40%)
X B(7, 0.4)
p=0.4, q=1-0.4 = 0.6

8. a)P(X=3)
= 0.2903
b)Probability at least two not accepted
1- P(X=0) + P(X=1)
=1- (0.0280 + 0.1306)
= 1- 0.1586
= 0. 8414
3
7
3
3
7
)
4
.
0
1
(
)
4
.
0
( 

C
]
)
4
.
0
1
(
)
4
.
0
(
)
4
.
0
1
(
)
4
.
0
(
[
1 1
7
1
1
7
0
7
0
0
7 





 C
C

9. •Mean,
•Variance,
•Standard deviation,
npq

2

npq



10. EXAMPLES
1)A test has 50 multiple choice questions with 5
different option of answers for each questions.
Given that there is only one right answer for each
question and the answer to each question are
done by guessing, find the
a) the mean of right answer
b) the standard deviation of right answer

11. SOLUTION
= 10
npq

2

b)
=
= 8
=
2.8284
8



12. 2) X is a binomial random variable such
that . If its mean and standard
deviation are 60 and 3 respectively.
Find the value p and n.

13. SOLUTION
Mean = 60
np = 60
Std dev = 3
5
3

npq
𝑛𝑝𝑞=(3 √5)
2
60 q = 45
q =
p =
np = 60
n = 240

14. GRAPH OF BINOMIAL DISTRIBUTION
• Success book page 427

15. 8.2 NORMAL DISTRIBUTION
•Parameters:
•P(a < X < b) = area under the curve in range
of a and b.
•Graph of normal
• = Standard normal distribution

16. •Convert Normal to standard normal
Z = standard score/ z-score
X = value of normal rv
= mean
= std dev

17. EXAMPLES
1) A normal distribution has a mean, =8 and
a std dev, =2. calculate the standard score of
value X = 13.

18. 2) The masses of students of a 5 Broadcaster
class members are normally distributed with
a mean of 60kg and a standard deviation
of 15kg. Find
a)The standard score of the mass of 65kg.
b)The mass of a student that corresponds to
the standard score -

19. SOLUTION
a)

20. b)

21. HOMEWORK
•Page 440 - Question 1 and 2 only
•Page 442 – Question 12 and 13
•Page 443 - Question 8 and 9