presentation on teaching math on grade 11

1. STATISTICS
and
PROBABILITY
MRS. JONNAH MARIZ NACAR-BERNAL
M AT H E M AT I C S 1 1

2. KEEP QUIET WHEN
SOMEONE IS TALKING
CLA SS RU LE

3. CLA SS RU LE
RAISE HAND IF YOU
WANT TO SHARE SOME
IDEAS

4. NO USING OF
CELLPHONES
CLA SS RU LE

5. Q UI CK REV I EW
PROPERTIES OF A
NORMAL DISTRIBUTION

6. PROPERTIES OF A
NORMAL DISTRIBUTION

7. SHORT
EXERCISE

8. Yes or
No
Game
stats and prob edition

9. The
Rules
•Answer the
questions within 10
second
•If the answer is
correct the GROUP
will get 1 point
•if the answer is wrong
the GROUP will lose 1
point
•Have fun!

10. The expression 68% is the
same as 0.68
The Question
You have 10 seconds

11. Yes
The
Answer

12. a probability value is a
number from 0 to 1
The Question
You have 10 seconds

13. Yes
The
Answer

14. the scores at the base
line of the normal curve
are called x
The
Question
You have 10 seconds

15. No
The
Answer
z - values

16. the normal curve is
a probability
distribution
The
Question
You have 10 seconds

17. Yes
The
Answer

18. the normal curve is
asymmetrical
The
Question
You have 10 seconds

19. No
The
Answer
it is symmetrical

20. Good Job
Everyone!!

21. Random Variables
And
Probability
Distribution
S T A T I S T I C S
a n d
P R O B A B I L I T Y

22. LEA RN IN G
O BJE CTI V ES
a.Identify regions under the normal curve
corresponding to the different standard
normal values;
b.Find the area under the normal curve either to
the right or left of the given standard normal
value; and
c.Perform finding the area under the normal
curve with accuracy and patience

23. M A T H E M A T I C S
1 1
Figure A
= 45
= 6
Figure B
= 0
= 1

24. M A T H E M A T I C S
1 1
Figure 1 has a raw values, not standardized while
figure 2 is in standardized normal distribution
values
CONCLUSION

25. - A random variable that has a normal distribution with
a mean of zero and a standard deviation of one.
- The letter z is commonly used to designate the normal
random variable.
S t a n d a r d N o r m a l
D i s t r i b u t i o n

26. W h y d o w e n e e d t o
s t a n d a r d i z e d t h e v a l u e s ?

27. - A normal variable is standardized to simplify the
process in approximating areas for normal curves.
- a table was created to summarize the areas under the
standard normal curve and to further simplify the
process. This table of probabilities is known as the z-
table.
S t a n d a r d N o r m a l
D i s t r i b u t i o n

28. S t a n d a r d N o r m a l
D i s t r i b u t i o n

29. - The intersection of the
columns and rows that
contain the digits of the
scores
- A cell that has a total area
from the left end of the
normal curve to the z-scores
Z - t a b l e

30. -3 -2 -1 0 1 2 3
1. shade the area
between 1 and 2.
2. Shade the area
between -1 and -3
3. Area between 0
and 2
Task

31. The z-table provides the section of the
area between any two specific values
under the curve, regions under the curve
can be described in terms of area.
Z - t a b l e

32. How t o u s e t h e z -
t ab l e

33. Find the area that corresponds to z =
1.85.
EX AM P LE

34. Find the area that corresponds to z =
1.85.
STEP
S
1. LOCATE the first two digits in the leftmost
column
2. The last digit is found at the first row of the
table
3. Find their intersection which gives the
corresponding area from the mean

35. Find the area that corresponds to z =
1.85
1. LOCATE the first two digits in the leftmost
column
2. The last digit is found at the first row of the
table

36. Find the area that corresponds to z =
1.85
3. Find their intersection which gives the
corresponding area from the mean
This means that the area of the z score of 1.85 from
the mean is 0.46784 or 46.78%.

37. Find the area that corresponds to z = 2.67, can someone
answer?
This means that the area of the z score of 1.85 from
the mean is 0.49621 or 49.62%.

38. Determine the area under the standard normal
curve to the right of 1.63.
STEPS

39. 0.5 – 0.44845 =
0.05155 or 5.15%
ANSWER
Determine the area under the standard normal
curve to the right of 1.63.

40. Determine the area under the standard normal
curve to the right of -0.67.
STEPS

41. 0.5 + 0.24857 =
0.77935 or 77.94%
ANSWER
Determine the area under the standard normal
curve to the right of -0.67.

42. C O N V E R T I N G T H E V A L U E O F X
I N T O Z - S C O R E S

43. Given a normal random variable X with mean (µ) and
standard deviation ( ), each value of x of the
𝜎
variable can be transformed into z-scores using the
formula

44. A random variable X has a mean of 6
and a standard deviation of 2. Find the
corresponding z- score for x = 11.
EX AM P LE
ANSWER
z = 2.5

45. A random variable X has a mean of 6
and a standard deviation of 2. Find the
corresponding z- score for x = 11.
EX AM P LE

46. A random variable X has a mean of
28 and a standard deviation of 5. Find
the corresponding z- score for x = 18.
EX AM P LE
ANSWER
z = -2
0.47725 or 47.73%

47. Let x be a normally distributed random
variable with a mean of 10 and a standard
deviation of 2. Find the probability that x
lies between 11 and 13.6.
EX AM P LE
ANSWER
z = 1.3
0.40320 or 40.32%

48. Directions: complete the given diagram
below by filling up the necessary details
about the steps in finding the probability
using the standard normal curve and
finding the z - scores
AC T I V I T Y
Work by pairs

49. Directions: complete the given diagram below by filling up the necessary details
about the steps in finding the probability using the standard normal curve and
finding the z - scores

50. EN D O F T HE LE SSO N